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Last release check: all 3,368 checks passed on calculation engine 8, 2026-11-13.
An example
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5kN/2m
2m5kN= 2.5 kN/m
25kN⋅m= 2.5 kN·m
Every check, case by case
The whole register, in one table
Nothing here is folded away. 355 named cases and 3,000 random formulas, in one list: the formula as MathCanvas shows it, the answer worked out separately, what MathCanvas gives, and where the answer comes from. Running is done in your browser and nothing is sent to us; rows turn green or red as the run reaches them.
| # | Check | In MathCanvas | Should be | MathCanvas gives | Where it comes from |
|---|---|---|---|---|---|
| Everyday formulasReal worksheets, easy first. Each starts from its inputs, and every way of writing the formula must give the same answer.14 formulas, 9 worksheetsNot run yet | |||||
Load combination and self-weightG_{k} := 10\frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}}Q_{k} := 5\frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}}\rho_{c} := 25\frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}^{3}}h := 0.2\operatorname{\textcolor{blue}{m}} | |||||
| 1 | E_d = 1.35·G_k + 1.5·Q_k | 1.35\cdot G_{k}+1.5\cdot Q_{k}Also written as 1.35G_{k}+1.5Q_{k} | 21 kN/m | — Not run yet | EN 1990, (6.10) |
| 2 | g = ρ·h | \rho_{c}\cdot h | 5 kN/m² | — Not run yet | Self-weight |
Roof snow load\mu_{1} := 0.8C_{e} := 1.0C_{t} := 1.0s_{k} := 1.0\frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}^{2}} | |||||
| 3 | s = μ₁·C_e·C_t·s_k | \mu_{1}\cdot C_{e}\cdot C_{t}\cdot s_{k} | 0.8 kN/m² | — Not run yet | EN 1991-1-3, (5.1) |
Thermal elongation\alpha_{T} := 12\cdot 10^{-6}\operatorname{\textcolor{blue}{K}}^{-1}\Delta T := 30\operatorname{\textcolor{blue}{K}}L_{0} := 10\operatorname{\textcolor{blue}{m}} | |||||
| 4 | ΔL = α·ΔT·L | \alpha_{T}\cdot\Delta T\cdot L_{0} | 3.6 mm | — Not run yet | Linear thermal expansion |
Simply supported beam, uniform loadq := 12\frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}}L := 6\operatorname{\textcolor{blue}{m}}E := 210\operatorname{\textcolor{blue}{GPa}}I := 8356\operatorname{\textcolor{blue}{cm}}^{4} | |||||
| 5 | M = qL²/8 | \frac{q\cdot L^{2}}{8}Also written as \frac{1}{8}\cdot q\cdot L^{2}0.125\cdot q\cdot L^{2} | 54 kN·m | — Not run yet | Beam statics |
| 6 | V = qL/2 | \frac{q\cdot L}{2}Also written as \frac{q}{2}\cdot L0.5\cdot q\cdot L | 36 kN | — Not run yet | Beam statics |
| 7 | δ = 5qL⁴/(384EI) | \frac{5\cdot q\cdot L^{4}}{384\cdot E\cdot I}Also written as \frac{5}{384}\cdot\frac{q\cdot L^{4}}{E\cdot I}\frac{5}{384}\cdot\frac{q L^{4}}{E I} | 11.54 mm | — Not run yet | Beam statics |
Steel bending resistance and utilisationW_{pl} := 628.4\operatorname{\textcolor{blue}{cm}}^{3}f_{y} := 235\operatorname{\textcolor{blue}{MPa}}\gamma_{M0} := 1.0M_{Ed} := 54\operatorname{\textcolor{blue}{kN}}\cdot \operatorname{\textcolor{blue}{m}} | |||||
| 8 | M_c,Rd = W_pl·f_y/γ_M0 | M_{c,Rd} := \frac{W_{pl}\cdot f_{y}}{\gamma_{M0}}Also written as W_{pl}\cdot\frac{f_{y}}{\gamma_{M0}} | 147.674 kN·m | — Not run yet | EN 1993-1-1, 6.2.5 (6.13) |
| 9 | η = M_Ed/M_c,Rd | \frac{M_{Ed}}{M_{c,Rd}} | 0.36567 | — Not run yet | Utilisation |
Bolt shear resistance, M20 8.8\alpha_{v} := 0.6f_{ub} := 800\operatorname{\textcolor{blue}{MPa}}A_{s} := 245\operatorname{\textcolor{blue}{mm}}^{2}\gamma_{M2} := 1.25 | |||||
| 10 | F_v,Rd = α_v·f_ub·A_s/γ_M2 | \frac{\alpha_{v}\cdot f_{ub}\cdot A_{s}}{\gamma_{M2}}Also written as \alpha_{v}\cdot f_{ub}\cdot\frac{A_{s}}{\gamma_{M2}} | 94.08 kN | — Not run yet | EN 1993-1-8, Table 3.4 |
Concrete design strength and relative moment\alpha_{cc} := 1.0f_{ck} := 30\operatorname{\textcolor{blue}{MPa}}\gamma_{c} := 1.5M_{Ed} := 120\operatorname{\textcolor{blue}{kN}}\cdot \operatorname{\textcolor{blue}{m}}b := 300\operatorname{\textcolor{blue}{mm}}d := 450\operatorname{\textcolor{blue}{mm}} | |||||
| 11 | f_cd = α_cc·f_ck/γ_c | f_{cd} := \frac{\alpha_{cc}\cdot f_{ck}}{\gamma_{c}}Also written as \alpha_{cc}\cdot\frac{f_{ck}}{\gamma_{c}} | 20 MPa | — Not run yet | EN 1992-1-1, 3.1.6 (3.15) |
| 12 | μ = M_Ed/(b·d²·f_cd) | \frac{M_{Ed}}{b\cdot d^{2}\cdot f_{cd}}Also written as \frac{\frac{M_{Ed}}{b\cdot d^{2}}}{f_{cd}} | 0.0987654 | — Not run yet | Rectangular section design |
Euler critical loadE := 210\operatorname{\textcolor{blue}{GPa}}I := 8356\operatorname{\textcolor{blue}{cm}}^{4}L_{cr} := 6\operatorname{\textcolor{blue}{m}} | |||||
| 13 | N_cr = π²EI/L_cr² | \frac{\operatorname{\pi}^{2}\cdot E\cdot I}{L_{cr}^{2}}Also written as \operatorname{\pi}^{2}\cdot\frac{E\cdot I}{L_{cr}^{2}} | 4810.77 kN | — Not run yet | Elastic buckling |
Imperial beam, uniform load (US units)w := 1.2\frac{\operatorname{\textcolor{blue}{kip}}}{\operatorname{\textcolor{blue}{ft}}}L_{s} := 20\operatorname{\textcolor{blue}{ft}} | |||||
| 14 | M = wL²/8 | \frac{w\cdot L_{s}^{2}}{8}Also written as \frac{1}{8}\cdot w\cdot L_{s}^{2} | 60 kip·ft | — Not run yet | Beam statics, US customary units |
| Official worked examplesAnswers printed in European Commission design handbooks and NIST’s certified data, each evaluated from the inputs as printed.106 cases from 3 handbooksNot run yet | |||||
| 15 | N_c,RdA·f_y/γ_M0 | \frac{170.9\operatorname{cm}^{2}\cdot 355\operatorname{MPa}}{1.00} | 6067,0 kN | — Not run yet | JRC EUR 27346 EN (2015)§1.3.3.2, Example 3: HEB 340 column, S 355 (L. Simões da Silva, R. Simões), PDF p. 63 |
| 16 | λ₁π·√(E/f_y) | \operatorname{\pi}\cdot\sqrt{\frac{210\operatorname{GPa}}{355\operatorname{MPa}}} | 76,41 | — Not run yet | JRC EUR 27346 EN (2015)§1.3.3.2, Example 3: HEB 340 column, S 355 (L. Simões da Silva, R. Simões), PDF p. 63 |
| 17 | λ_zL_Ez/i_z | \frac{4.335\operatorname{m}}{7.53\operatorname{cm}} | 57,57 | — Not run yet | JRC EUR 27346 EN (2015)§1.3.3.2, Example 3: HEB 340 column, S 355 (L. Simões da Silva, R. Simões), PDF p. 63 |
| 18 | λ̄_zλ_z/λ₁ | \frac{57.57}{76.41} | 0,75 | — Not run yet | JRC EUR 27346 EN (2015)§1.3.3.2, Example 3: HEB 340 column, S 355 (L. Simões da Silva, R. Simões), PDF p. 63 |
| 19 | Φ_z0.5·[1 + α(λ̄_z − 0.2) + λ̄_z²] | 0.5\cdot\left(1+0.49\cdot\left(0.75-0.2\right)+0.75^{2}\right) | 0,92 | — Not run yet | JRC EUR 27346 EN (2015)§1.3.3.2, Example 3: HEB 340 column, S 355 (L. Simões da Silva, R. Simões), PDF p. 63 |
| 20 | χ_z1/(Φ_z + √(Φ_z² − λ̄_z²)) | \frac{1}{0.92+\sqrt{0.92^{2}-0.75^{2}}} | 0,69 | — Not run yet | JRC EUR 27346 EN (2015)§1.3.3.2, Example 3: HEB 340 column, S 355 (L. Simões da Silva, R. Simões), PDF p. 63 |
| 21 | N_b,Rdχ·A·f_y/γ_M1 | \frac{0.69\cdot 170.9\operatorname{cm}^{2}\cdot 355\operatorname{MPa}}{1.00} | 4186,2 kN | — Not run yet | JRC EUR 27346 EN (2015)§1.3.3.2, Example 3: HEB 340 column, S 355 (L. Simões da Silva, R. Simões), PDF p. 63 |
| 22 | M_c,RdW_pl,y·f_y/γ_M0 | \frac{1307\operatorname{cm}^{3}\cdot 355\operatorname{MPa}}{1.00} | 464,0 kNm | — Not run yet | JRC EUR 27346 EN (2015)§1.3.4.2: IPE 400 beam, S 355 (L. Simões da Silva, R. Simões), PDF p. 74 |
| 23 | V_pl,RdA_v·f_y/(√3·γ_M0) | \frac{42.69\operatorname{cm}^{2}\cdot 355\operatorname{MPa}}{\sqrt{3}\cdot 1.00} | 875,0 kN | — Not run yet | JRC EUR 27346 EN (2015)§1.3.4.2: IPE 400 beam, S 355 (L. Simões da Silva, R. Simões), PDF p. 74 |
| 24 | λ̄_LT√(W_y·f_y/M_cr) | \sqrt{\frac{1307\operatorname{cm}^{3}\cdot 355\operatorname{MPa}}{164.7\operatorname{kN}\cdot\operatorname{m}}} | 1,68 | — Not run yet | JRC EUR 27346 EN (2015)§1.3.4.2: IPE 400 beam, S 355 (L. Simões da Silva, R. Simões), PDF p. 74 |
| 25 | Φ_LT0.5·[1 + α_LT(λ̄_LT − 0.2) + λ̄_LT²] | 0.5\cdot\left(1+0.34\cdot\left(1.68-0.2\right)+1.68^{2}\right) | 2,16 | — Not run yet | JRC EUR 27346 EN (2015)§1.3.4.2: IPE 400 beam, S 355 (L. Simões da Silva, R. Simões), PDF p. 74 |
| 26 | χ_LT1/(Φ_LT + √(Φ_LT² − λ̄_LT²)) | \frac{1}{2.16+\sqrt{2.16^{2}-1.68^{2}}} | 0,28 | — Not run yet | JRC EUR 27346 EN (2015)§1.3.4.2: IPE 400 beam, S 355 (L. Simões da Silva, R. Simões), PDF p. 74 |
| 27 | M_b,Rdχ_LT·W_pl,y·f_y/γ_M1 | \frac{0.28\cdot 1307\operatorname{cm}^{3}\cdot 355\operatorname{MPa}}{1.00} | 129,9 kNm | — Not run yet | JRC EUR 27346 EN (2015)§1.3.4.2: IPE 400 beam, S 355 (L. Simões da Silva, R. Simões), PDF p. 74 |
| 28 | V_pl,Rd (beam web)A_v·f_y/(√3·γ_M0) | \frac{6.2\operatorname{mm}\cdot 130\operatorname{mm}\cdot 235\operatorname{MPa}}{\sqrt{3}\cdot 1.00} | 109,4 kN | — Not run yet | JRC EUR 27346 EN (2015)§2.2.7: header plate connection (F. Wald), PDF p. 120 |
| 29 | F_v,Rd (M16, 4.6)α_v·A_s·f_ub/γ_M2 | \frac{0.6\cdot 157\operatorname{mm}^{2}\cdot 400\operatorname{MPa}}{1.25} | 30,1 kN | — Not run yet | JRC EUR 27346 EN (2015)§2.2.7: header plate connection (F. Wald), PDF p. 120 |
| 30 | F_w,Rd (fillet welds)2·a·L·f_u/(√3·β_w·γ_M2) | \frac{2\cdot 3\operatorname{mm}\cdot 130\operatorname{mm}\cdot 360\operatorname{MPa}}{\sqrt{3}\cdot 0.8\cdot 1.25} | 162,1 kN | — Not run yet | JRC EUR 27346 EN (2015)§2.2.7: header plate connection (F. Wald), PDF p. 121 |
| 31 | F_v,Rd (M20)α_v·A_s·f_ub/γ_M2 | \frac{0.6\cdot 245\operatorname{mm}^{2}\cdot 500\operatorname{MPa}}{1.25} | 58,8 kN | — Not run yet | JRC EUR 27346 EN (2015)§2.2.8: fin plate connection (F. Wald), PDF p. 122 |
| 32 | F_b,Rd (beam web)k₁·α_b·d·t·f_u/γ_M2 | \frac{2.5\cdot 0.659\cdot 20\operatorname{mm}\cdot 5.6\operatorname{mm}\cdot 360\operatorname{MPa}}{1.25} | 53,1 kN | — Not run yet | JRC EUR 27346 EN (2015)§2.2.8: fin plate connection (F. Wald), PDF p. 122 |
| 33 | V_eff,2,Rd (fin plate)0.5·A_nt·f_u/γ_M2 + A_nv·f_y/(√3·γ_M0) | \frac{0.5\cdot 290\operatorname{mm}^{2}\cdot 360\operatorname{MPa}}{1.25}+\frac{670\operatorname{mm}^{2}\cdot 235\operatorname{MPa}}{\sqrt{3}\cdot 1.00} | 132,7 kN | — Not run yet | JRC EUR 27346 EN (2015)§2.2.8: fin plate connection (F. Wald), PDF p. 124 |
| 34 | V_pl,Rd (fin plate)A_v·f_y/(√3·γ_M0) | \frac{10\operatorname{mm}\cdot 140\operatorname{mm}\cdot 235\operatorname{MPa}}{\sqrt{3}\cdot 1.00} | 189,9 kN | — Not run yet | JRC EUR 27346 EN (2015)§2.2.8: fin plate connection (F. Wald), PDF p. 124 |
| 35 | V_eff,2,Rd (beam web)0.5·A_nt·f_u/γ_M2 + A_nv·f_y/(√3·γ_M0) | \frac{0.5\cdot 162.4\operatorname{mm}^{2}\cdot 360\operatorname{MPa}}{1.25}+\frac{515.2\operatorname{mm}^{2}\cdot 235\operatorname{MPa}}{\sqrt{3}\cdot 1.00} | 93,3 kN | — Not run yet | JRC EUR 27346 EN (2015)§2.2.8: fin plate connection (F. Wald), PDF p. 124 |
| 36 | M_el,Rd (fin plate)W_el·f_y/γ_M0, W_el = t·h²/6 | \frac{\frac{10\operatorname{mm}\cdot\left(140\operatorname{mm}\right)^{2}}{6}\cdot 235\operatorname{MPa}}{1.00} | 7,7 kNm | — Not run yet | JRC EUR 27346 EN (2015)§2.2.8: fin plate connection (F. Wald), PDF p. 124 |
| 37 | b_eff,1 (mid-span)0.2·b₁ + 0.1·(0.85·l) | 0.2\cdot 2875\operatorname{mm}+0.1\cdot\left(0.85\cdot 7125\operatorname{mm}\right) | 1181 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.1: effective width of the T-beam in axis 2 (J. Walraven, S. Gmainer), PDF p. 66 |
| 38 | b_eff (mid-span)2·b_eff,1 + b_w | 2\cdot\left(0.2\cdot 2875\operatorname{mm}+0.1\cdot 0.85\cdot 7125\operatorname{mm}\right)+250\operatorname{mm} | 2611 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.1: effective width of the T-beam in axis 2 (J. Walraven, S. Gmainer), PDF p. 66 |
| 39 | b_eff,1 (support)0.2·b₁ + 0.1·(0.30·l) | 0.2\cdot 2875\operatorname{mm}+0.1\cdot\left(0.30\cdot 7125\operatorname{mm}\right) | 789 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.1: effective width of the T-beam in axis 2 (J. Walraven, S. Gmainer), PDF p. 66 |
| 40 | b_eff (support)2·b_eff,1 + b_w | 2\cdot 788.8\operatorname{mm}+250\operatorname{mm} | 1828 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.1: effective width of the T-beam in axis 2 (J. Walraven, S. Gmainer), PDF p. 66 |
| 41 | K (mid-span)M_Ed/(b·d²·f_cd) | \frac{89.3\operatorname{kN}\cdot\operatorname{m}}{2611.2\operatorname{mm}\cdot\left(372\operatorname{mm}\right)^{2}\cdot\frac{25\operatorname{MPa}}{1.5}} | 0,0148 | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.3: bending reinforcement of the T-beam (J. Walraven, S. Gmainer), PDF p. 70 |
| 42 | z/d (mid-span)0.5·(1 + √(1 − 2K)) | 0.5\cdot\left(1+\sqrt{1-2\cdot 0.0148}\right) | 0,9925 | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.3: bending reinforcement of the T-beam (J. Walraven, S. Gmainer), PDF p. 70 |
| 43 | A_sl (mid-span)M_Ed/(f_yd·z) | \frac{89.3\operatorname{kN}\cdot\operatorname{m}}{435\operatorname{MPa}\cdot 372\operatorname{mm}\cdot 0.9925} | 556 mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.3: bending reinforcement of the T-beam (J. Walraven, S. Gmainer), PDF p. 70 |
| 44 | K (support)M_Ed/(b·d²·f_cd) | \frac{132.9\operatorname{kN}\cdot\operatorname{m}}{250\operatorname{mm}\cdot\left(372\operatorname{mm}\right)^{2}\cdot\frac{25\operatorname{MPa}}{1.5}} | 0,230 | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.3: bending reinforcement of the T-beam (J. Walraven, S. Gmainer), PDF p. 70 |
| 45 | z/d (support)0.5·(1 + √(1 − 2K)) | 0.5\cdot\left(1+\sqrt{1-2\cdot 0.230}\right) | 0,867 | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.3: bending reinforcement of the T-beam (J. Walraven, S. Gmainer), PDF p. 70 |
| 46 | A_sl (support)M_Ed/(f_yd·z) | \frac{132.9\operatorname{kN}\cdot\operatorname{m}}{435\operatorname{MPa}\cdot 372\operatorname{mm}\cdot 0.867} | 947 mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.3: bending reinforcement of the T-beam (J. Walraven, S. Gmainer), PDF p. 70 |
| 47 | A_s (4ϕ14)4·πϕ²/4 | 4\cdot\frac{\operatorname{\pi}\cdot\left(14\operatorname{mm}\right)^{2}}{4} | 616 mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.3: bending reinforcement of the T-beam (J. Walraven, S. Gmainer), PDF p. 70 |
| 48 | A_s (9ϕ12)9·πϕ²/4 | 9\cdot\frac{\operatorname{\pi}\cdot\left(12\operatorname{mm}\right)^{2}}{4} | 1018 mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.3: bending reinforcement of the T-beam (J. Walraven, S. Gmainer), PDF p. 70 |
| 49 | V_Ed,redV_Ed·(a − d)/a | 129.9\operatorname{kN}\cdot\frac{3.36\operatorname{m}-0.372\operatorname{m}}{3.36\operatorname{m}} | 115,52 kN | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear design of the T-beam at support A (J. Walraven, S. Gmainer), PDF p. 71 |
| 50 | k1 + √(200/d) | 1+\sqrt{\frac{200}{372}} | 1,73 | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear design of the T-beam at support A (J. Walraven, S. Gmainer), PDF p. 71 |
| 51 | ρ_lA_sl/(b_w·d) | \frac{565\operatorname{mm}^{2}}{250\operatorname{mm}\cdot 372\operatorname{mm}} | 0,0061 | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear design of the T-beam at support A (J. Walraven, S. Gmainer), PDF p. 71 |
| 52 | V_Rd,cC_Rd,c·k·(100·ρ_l·f_ck)^(1/3)·b_w·d | 0.12\cdot\left(1+\sqrt{\frac{200}{372}}\right)\cdot\left(100\cdot\frac{565}{250\cdot 372}\cdot 25\right)^{\frac{1}{3}}\cdot\operatorname{MPa}\cdot 250\operatorname{mm}\cdot 372\operatorname{mm} | 47,90 kN | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear design of the T-beam at support A (J. Walraven, S. Gmainer), PDF p. 71 |
| 53 | A_sw/sV_Ed/(z·f_ywd·cot θ) | \frac{115.52\operatorname{kN}}{0.9\cdot 0.372\operatorname{m}\cdot 435\operatorname{MPa}\cdot 2.5} | 317 mm²/m | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear design of the T-beam at support A (J. Walraven, S. Gmainer), PDF p. 72 |
| 54 | a_sw,min0.08·√f_ck/f_yk·b_w | 0.08\cdot\frac{\sqrt{25}}{500}\cdot 0.25\operatorname{m} | 200 mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear design of the T-beam at support A (J. Walraven, S. Gmainer), PDF p. 72 |
| 55 | ν0.6·(1 − f_ck/250) | 0.6\cdot\left(1-\frac{25}{250}\right) | 0,54 | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear design of the T-beam at support A (J. Walraven, S. Gmainer), PDF p. 72 |
| 56 | V_Rd,maxb_w·z·ν·f_cd/(cot θ + tan θ) | 0.25\operatorname{m}\cdot 0.9\cdot 0.372\operatorname{m}\cdot 0.54\cdot\frac{25\operatorname{MPa}}{1.5}\cdot\frac{1}{2.5+0.4} | 259,8 kN | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear design of the T-beam at support A (J. Walraven, S. Gmainer), PDF p. 72 |
| 57 | f_ctdα_ct·f_ctk,0.05/γ_c | \frac{1.0\cdot 1.8\operatorname{MPa}}{1.5} | 1,2 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 74 |
| 58 | ν_Ed,A½(b_eff − b_w)/b_eff · V_Ed/(z·h_f) | \frac{\frac{1}{2}\cdot\left(2611.2-250\right)}{2611.2}\cdot\frac{115520\operatorname{N}}{0.9\cdot 372\operatorname{mm}\cdot 180\operatorname{mm}} | 0,87 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 74 |
| 59 | ν_Ed,C½(b_eff − b_w)/b_eff · V_Ed/(z·h_f) | \frac{\frac{1}{2}\cdot\left(2611.2-250\right)}{2611.2}\cdot\frac{89830\operatorname{N}}{0.9\cdot 372\operatorname{mm}\cdot 180\operatorname{mm}} | 0,67 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 74 |
| 60 | ν_Ed,B,left½(b_eff − b_w)/b_eff · V_Ed/(z·h_f) | \frac{\frac{1}{2}\cdot\left(1827.6-250\right)}{1827.6}\cdot\frac{101830\operatorname{N}}{0.9\cdot 372\operatorname{mm}\cdot 180\operatorname{mm}} | 0,73 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 75 |
| 61 | ν_Ed,B,right½(b_eff − b_w)/b_eff · V_Ed/(z·h_f) | \frac{\frac{1}{2}\cdot\left(1827.6-250\right)}{1827.6}\cdot\frac{131410\operatorname{N}}{0.9\cdot 372\operatorname{mm}\cdot 180\operatorname{mm}} | 0,94 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 75 |
| 62 | A_st/s (support A)½(b_eff − b_w)/b_eff · V_Ed/(z·f_yd·cot θ_f) | \frac{\frac{1}{2}\cdot\left(2611.2-250\right)}{2611.2}\cdot\frac{115520\operatorname{N}}{0.9\cdot 372\operatorname{mm}\cdot 435\operatorname{MPa}}\cdot\frac{1}{2.0} | 0,18 mm²/mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 75 |
| 63 | A_st/s (support C)½(b_eff − b_w)/b_eff · V_Ed/(z·f_yd·cot θ_f) | \frac{\frac{1}{2}\cdot\left(2611.2-250\right)}{2611.2}\cdot\frac{89830\operatorname{N}}{0.9\cdot 372\operatorname{mm}\cdot 435\operatorname{MPa}}\cdot\frac{1}{2.0} | 0,14 mm²/mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 75 |
| 64 | A_st/s (support B, left)½(b_eff − b_w)/b_eff · V_Ed/(z·f_yd·cot θ_f) | \frac{\frac{1}{2}\cdot\left(1827.6-250\right)}{1827.6}\cdot\frac{101830\operatorname{N}}{0.9\cdot 372\operatorname{mm}\cdot 435\operatorname{MPa}}\cdot\frac{1}{2.0} | 0,15 mm²/mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 75 |
| 65 | A_st/s (support B, right)½(b_eff − b_w)/b_eff · V_Ed/(z·f_yd·cot θ_f) | \frac{\frac{1}{2}\cdot\left(1827.6-250\right)}{1827.6}\cdot\frac{131410\operatorname{N}}{0.9\cdot 372\operatorname{mm}\cdot 435\operatorname{MPa}}\cdot\frac{1}{2.0} | 0,19 mm²/mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 76 |
| 66 | ϕ8/250(πϕ²/4)/s | \frac{\operatorname{\pi}\cdot\left(8\operatorname{mm}\right)^{2}}{4\cdot 250\operatorname{mm}} | 0,20 mm²/mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.4: shear between web and flanges of the T-beam (J. Walraven, S. Gmainer), PDF p. 75 |
| 67 | G_Ed1.3·(G₁ + G₂) | 1.3\cdot\left(4.5+3.0\right)\cdot\frac{\operatorname{kN}}{\operatorname{m}^{2}} | 9,75 kN/m² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.5: design of slabs supported by beams (J. Walraven, S. Gmainer), PDF p. 76 |
| 68 | L_Ed1.3·(G₁ + G₂) + 1.5·Q | 1.3\cdot\left(4.5\frac{\operatorname{kN}}{\operatorname{m}^{2}}+3.0\frac{\operatorname{kN}}{\operatorname{m}^{2}}\right)+1.5\cdot 2.0\frac{\operatorname{kN}}{\operatorname{m}^{2}} | 12,75 kN/m² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.1.5: design of slabs supported by beams (J. Walraven, S. Gmainer), PDF p. 76 |
| 69 | d_yh − c − ϕ/2 | 210\operatorname{mm}-30\operatorname{mm}-\frac{16\operatorname{mm}}{2} | 172 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 83 |
| 70 | d_zh − c − ϕ − ϕ/2 | 210\operatorname{mm}-30\operatorname{mm}-16\operatorname{mm}-\frac{16\operatorname{mm}}{2} | 156 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 83 |
| 71 | ν_Rd,max0.4·ν·f_cd | 0.4\cdot 0.54\cdot\frac{25\operatorname{MPa}}{1.5} | 3,6 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 84 |
| 72 | ν_Ed (perimeter u₀)β·V_Ed/(u₀·d) | \frac{1.15\cdot 705\operatorname{kN}}{4\cdot 500\operatorname{mm}\cdot 164\operatorname{mm}} | 2,47 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 84 |
| 73 | u₁4·c + 2π·2d | 4\cdot 500\operatorname{mm}+2\cdot\operatorname{\pi}\cdot 2\cdot 164\operatorname{mm} | 4061 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 84 |
| 74 | ν_Ed (perimeter u₁)β·V_Ed/(u₁·d) | \frac{1.15\cdot 705\operatorname{kN}}{4061\operatorname{mm}\cdot 164\operatorname{mm}} | 1,22 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 84 |
| 75 | k (punching)1 + √(200/d) | 1+\sqrt{\frac{200}{164}} | 2,10 | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 85 |
| 76 | ν_Rd,cC_Rd,c·k·(100·ρ_l·f_ck)^(1/3) | 0.12\cdot 2.0\cdot\left(100\cdot 0.0083\cdot 25\right)^{\frac{1}{3}}\cdot\operatorname{MPa} | 0,66 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 85 |
| 77 | ν_min0.035·k^(3/2)·f_ck^(1/2) | 0.035\cdot 2.0^{\frac{3}{2}}\cdot 25^{\frac{1}{2}}\cdot\operatorname{MPa} | 0,49 N/mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 85 |
| 78 | A_sw (per perimeter)(ν_Ed − 0.75·ν_Rd,c)·u₁·s_r/(1.5·f_ywd,ef) | \frac{\left(1.22-0.75\cdot 0.66\right)\operatorname{MPa}\cdot 4060.88\operatorname{mm}\cdot 123\operatorname{mm}}{1.5\cdot 291\operatorname{MPa}} | 830 mm² | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 86 |
| 79 | u_outβ·V_Ed/(ν_Rd,c·d) | \frac{1.15\cdot 705\operatorname{kN}}{0.66\operatorname{MPa}\cdot 164\operatorname{mm}} | 7490 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 86 |
| 80 | a (outer perimeter)(u_out − 4h)/(2π) | \frac{7490.30\operatorname{mm}-4\cdot 500\operatorname{mm}}{2\cdot\operatorname{\pi}} | 874 mm | — Not run yet | JRC EUR 26566 EN (2014)§3.2.2.3: punching shear at column B2 (J. Walraven, S. Gmainer), PDF p. 86 |
| 81 | P_fi,d,t1.25·q·L | 1.25\cdot 23.135\frac{\operatorname{kN}}{\operatorname{m}}\cdot 7\operatorname{m} | 202,4 kN | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 134 |
| 82 | M_fi,d,tq·l²/2 + P·l/2 | \frac{1.12\frac{\operatorname{kN}}{\operatorname{m}}\cdot\left(3\operatorname{m}\right)^{2}}{2}+\frac{202.4\operatorname{kN}\cdot 3\operatorname{m}}{2} | 308,6 kNm | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 134 |
| 83 | ε (fire)0.85·√(235/f_y) | 0.85\cdot\sqrt{\frac{235}{275}} | 0,786 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 135 |
| 84 | 72ε72·0.85·√(235/f_y) | 72\cdot 0.85\cdot\sqrt{\frac{235}{275}} | 56,6 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 135 |
| 85 | 9ε9·0.85·√(235/f_y) | 9\cdot 0.85\cdot\sqrt{\frac{235}{275}} | 7,07 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 135 |
| 86 | M_pl,RdW_pl,y·f_y/γ_M0 | \frac{2088.47\cdot 10^{3}\operatorname{mm}^{3}\cdot 275\operatorname{MPa}}{1.0} | 574,3 kNm | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 136 |
| 87 | V_pl,RdA_v·(f_y/√3)/γ_M0 | \frac{4896\operatorname{mm}^{2}\cdot\frac{275\operatorname{MPa}}{\sqrt{3}}}{1.0} | 777,3 kN | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 136 |
| 88 | μ₀,MM_fi,d,t·γ_M0/(M_Rd·γ_M,fi) | \frac{308.6\operatorname{kN}\cdot\operatorname{m}\cdot 1.0}{574.3\operatorname{kN}\cdot\operatorname{m}\cdot 1.0} | 0,537 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 136 |
| 89 | μ₀,VV_fi,d,t·γ_M0/(V_Rd·γ_M,fi) | \frac{104.5\operatorname{kN}\cdot 1.0}{777.3\operatorname{kN}\cdot 1.0} | 0,134 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 136 |
| 90 | μ₀,M,κ (unprotected)μ₀,M·κ₁·κ₂ | 0.537\cdot 0.7\cdot 1.0 | 0,376 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 136 |
| 91 | μ₀ (unprotected)max(μ₀,M,κ; μ₀,V,κ) | \max\left(0.376,0.134\right) | 0,376 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 137 |
| 92 | θ_cr (unprotected)39.19·ln[1/(0.9674·μ₀^3.833) − 1] + 482 | 39.19\cdot\ln\left(\frac{1}{0.9674\cdot 0.376^{3.833}}-1\right)+482 | 629 °C | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 137 |
| 93 | θ_cr (from k_y,θ)600 + (0.47 − μ₀)/(0.47 − 0.23)·100 | 600+\frac{0.47-0.376}{0.47-0.23}\cdot 100 | 639 °C | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 137 |
| 94 | k_sh0.9·(A_m/V)_b/(A_m/V) | 0.9\cdot\frac{70}{107} | 0,589 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 137 |
| 95 | k_sh·(A_m/V)·Δt/(c_a·ρ_a)k_sh/(c_a·ρ_a)·(A_m/V)·Δt | \frac{0.589}{600\cdot 7850}\cdot 107\cdot 3 | 4,014·10⁻⁵ | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 137 |
| 96 | μ₀,M,κ (protected)μ₀,M·κ₁·κ₂ | \frac{308.6}{574.3}\cdot 0.85\cdot 1.0 | 0,457 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 138 |
| 97 | θ_cr (protected)39.19·ln[1/(0.9674·μ₀^3.833) − 1] + 482 | 39.19\cdot\ln\left(\frac{1}{0.9674\cdot 0.457^{3.833}}-1\right)+482 | 599 °C | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 139 |
| 98 | ϕ (sprayed protection)c_p·ρ_p/(c_a·ρ_a)·d_p·A_p/V | \frac{1200\cdot 350}{600\cdot 7850}\cdot 10\cdot 10^{-3}\cdot 107 | 0,0954 | — Not run yet | JRC EUR 26698 EN (2014)§2.8.5, Example 3: HEA 360 main beam in fire (B. Zhao), PDF p. 139 |
| 99 | P_fi,d,t (column)Σ(G_k + ψ₂Q_k): secondary + main beam | 14.105\cdot 7+202.4+1.12\cdot 6 | 307,9 kN | — Not run yet | JRC EUR 26698 EN (2014)§2.8.6.1, Example 4: central column in fire (B. Zhao), PDF p. 140 |
| 100 | b_fi (secondary beam)b − 2·(β_n·t + 7) | 120\operatorname{mm}-2\cdot\left(30\cdot 0.8\operatorname{mm}+7\operatorname{mm}\right) | 58 mm | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 238 |
| 101 | h_fi (secondary beam)h − (β_n·t + 7) | 260\operatorname{mm}-\left(30\cdot 0.8\operatorname{mm}+7\operatorname{mm}\right) | 229 mm | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 238 |
| 102 | W_fi (secondary beam)b_fi·h_fi²/6 | \frac{58\operatorname{mm}\cdot\left(229\operatorname{mm}\right)^{2}}{6} | 506,9·10³ mm³ | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 238 |
| 103 | M_d,fi (secondary beam)q_d,fi·s·ℓ²/8 | \frac{\left(0.17+0.09+1.32+0.06+0.28+1.0+0.3\cdot 2.0\right)\frac{\operatorname{kN}}{\operatorname{m}^{2}}\cdot 1.0\operatorname{m}\cdot\left(4.0\operatorname{m}\right)^{2}}{8} | 7,0 kNm | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 238 |
| 104 | σ_d,fi (secondary beam)M_d,fi/W_fi | \frac{\frac{\left(0.17+0.09+1.32+0.06+0.28+1.0+0.3\cdot 2.0\right)\frac{\operatorname{kN}}{\operatorname{m}^{2}}\cdot 1.0\operatorname{m}\cdot\left(4.0\operatorname{m}\right)^{2}}{8}}{\frac{58\operatorname{mm}\cdot\left(229\operatorname{mm}\right)^{2}}{6}} | 13,9 N/mm² | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 238 |
| 105 | b_fi (main beam)b − 2·(β_n·t + 7) | 160\operatorname{mm}-2\cdot\left(30\cdot 0.7\operatorname{mm}+7\operatorname{mm}\right) | 104 mm | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 238 |
| 106 | h_fi (main beam)h − (β_n·t + 7) | 735\operatorname{mm}-\left(30\cdot 0.7\operatorname{mm}+7\operatorname{mm}\right) | 707 mm | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 238 |
| 107 | W_fi (main beam)b_fi·h_fi²/6 | \frac{104\operatorname{mm}\cdot\left(707\operatorname{mm}\right)^{2}}{6} | 8664·10³ mm³ | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 239 |
| 108 | M_d,fi (main beam)q_d,fi·s·ℓ²/8 | \frac{\left(0.17+0.17+0.09+1.32+0.06+0.28+1.0+0.3\cdot 2.0\right)\frac{\operatorname{kN}}{\operatorname{m}^{2}}\cdot 4.0\operatorname{m}\cdot\left(8.0\operatorname{m}\right)^{2}}{8} | 118,1 kNm | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 239 |
| 109 | σ_d,fi (main beam)M_d,fi/W_fi | \frac{118.1\cdot 10^{6}\operatorname{N}\cdot\operatorname{mm}}{8664\cdot 10^{3}\operatorname{mm}^{3}} | 13,6 N/mm² | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 239 |
| 110 | A_fi (column)b_fi·h_fi | \left(160\operatorname{mm}-2\cdot\left(30\cdot 0.8\operatorname{mm}+7\operatorname{mm}\right)\right)^{2} | 9604 mm² | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 239 |
| 111 | N_d,fi (column)q_d,fi·s·ℓ/2 | \frac{\left(0.17+0.17+0.09+1.32+0.06+0.28+1.0+0.3\cdot 2.0\right)\frac{\operatorname{kN}}{\operatorname{m}^{2}}\cdot 4.0\operatorname{m}\cdot 8.0\operatorname{m}}{2} | 59,0 kN | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 240 |
| 112 | σ_d,fi (column)N_d,fi/A_fi | \frac{59.0\cdot 10^{3}\operatorname{N}}{9604\operatorname{mm}^{2}} | 6,1 N/mm² | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 240 |
| 113 | i_fi (column)√(I_fi/A_fi) | \sqrt{\frac{\frac{98\operatorname{mm}\cdot\left(98\operatorname{mm}\right)^{3}}{12}}{98\operatorname{mm}\cdot 98\operatorname{mm}}} | 28,3 mm | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 240 |
| 114 | λ_fi (column)ℓ/i_fi | \frac{3000}{28.3} | 106,0 | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 240 |
| 115 | λ_rel,fi (column)λ_fi/π·√(f_c,0,k/E₀.₀₅), E₀.₀₅ = ⅔·E_mean | \frac{106.0}{3.14}\cdot\sqrt{\frac{21}{\frac{2}{3}\cdot 11000}} | 1,8 | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 240 |
| 116 | f_c,0,d,fi (column)k_fi·f_c,0,k·k_c,fi | 1.25\cdot 21.0\cdot 0.27 | 7,1 N/mm² | — Not run yet | JRC EUR 26698 EN (2014)§6.1.4: unprotected timber members, 30 minutes (A. Frangi), PDF p. 241 |
| 117 | Mean, NumAcc1mean of 3 eight-digit values | \operatorname{mean}\left(10000001,10000003,10000002\right) | 10000002 (exact) | — Not run yet | NIST StRDNumAcc1 (constructed, 3 values): certified values, NumAcc1.dat lines 41–43 |
| 118 | Standard deviation, NumAcc1sample standard deviation (n − 1) | \operatorname{std}\left(10000001,10000003,10000002\right) | 1 (exact) | — Not run yet | NIST StRDNumAcc1 (constructed, 3 values): certified values, NumAcc1.dat lines 41–43 |
| 119 | Mean, Mavromean of 50 measurements | \operatorname{mean}\left(2.00180,2.00170,2.00180,2.00190,2.00180,2.00170,2.00150,2.00140,2.00150,2.00150,2.00170,2.00180,2.00180,2.00190,2.00190,2.00210,2.00200,2.00160,2.00140,2.00130,2.00130,2.00150,2.00150,2.00160,2.00150,2.00140,2.00130,2.00140,2.00150,2.00140,2.00150,2.00160,2.00150,2.00160,2.00190,2.00200,2.00200,2.00210,2.00220,2.00230,2.00240,2.00250,2.00270,2.00260,2.00260,2.00260,2.00270,2.00260,2.00250,2.00240\right) | 2.00185600000000 | — Not run yet | NIST StRDMavro (filter transmittance, 50 values): certified values, Mavro.dat lines 41–43 |
| 120 | Standard deviation, Mavrosample standard deviation (n − 1) | \operatorname{std}\left(2.00180,2.00170,2.00180,2.00190,2.00180,2.00170,2.00150,2.00140,2.00150,2.00150,2.00170,2.00180,2.00180,2.00190,2.00190,2.00210,2.00200,2.00160,2.00140,2.00130,2.00130,2.00150,2.00150,2.00160,2.00150,2.00140,2.00130,2.00140,2.00150,2.00140,2.00150,2.00160,2.00150,2.00160,2.00190,2.00200,2.00200,2.00210,2.00220,2.00230,2.00240,2.00250,2.00270,2.00260,2.00260,2.00260,2.00270,2.00260,2.00250,2.00240\right) | 0.000429123454003053 | — Not run yet | NIST StRDMavro (filter transmittance, 50 values): certified values, Mavro.dat lines 41–43 |
| Unit definitionsEvery unit in the units list, against its official definition: the units panel, in full.104 unitsNot run yet | |||||
| 121 | 1 inin m | 1\operatorname{in} | 0.0254 m | — Not run yet | International inch (1959)Exact by definition |
| 122 | 1 ftin m | 1\operatorname{ft} | 0.3048 m | — Not run yet | International foot (1959)Exact by definition |
| 123 | 1 ydin m | 1\operatorname{yd} | 0.9144 m | — Not run yet | International yard (1959)Exact by definition |
| 124 | 1 miin m | 1\operatorname{mi} | 1609.344 m | — Not run yet | International mileExact by definition |
| 125 | 1 lbin kg | 1\operatorname{lb} | 0.45359237 kg | — Not run yet | Avoirdupois pound (1959)Exact by definition |
| 126 | 1 lbfin N | 1\operatorname{lbf} | 4.44822161526 N | — Not run yet | 1 lb × standard gravityFollows from defined units |
| 127 | 1 kipin kN | 1\operatorname{kip} | 4.44822161526 kN | — Not run yet | 1000 lbfFollows from defined units |
| 128 | 1 psiin Pa | 1\operatorname{psi} | 6894.75729317 Pa | — Not run yet | 1 lbf/in²Follows from defined units |
| 129 | 1 ksiin MPa | 1\operatorname{ksi} | 6.89475729317 MPa | — Not run yet | 1000 lbf/in²Follows from defined units |
| 130 | 1 psfin Pa | 1\operatorname{psf} | 47.8802589803 Pa | — Not run yet | 1 lbf/ft²Follows from defined units |
| 131 | 1 kip·ftin kN·m | 1\operatorname{kip}\cdot\operatorname{ft} | 1.35581794833 kN·m | — Not run yet | 1 kip × 1 ftFollows from defined units |
| 132 | 1 galin L | 1\operatorname{gal} | 3.785411784 L | — Not run yet | US liquid gallon (231 in³)Exact by definition |
| 133 | 1 gₙin m/s² | 1\operatorname{g_n} | 9.80665 m/s² | — Not run yet | Standard acceleration of gravityExact by definition |
| 134 | 1 kgfin N | 1\operatorname{kgf} | 9.80665 N | — Not run yet | 1 kg × standard gravityExact by definition |
| 135 | 1 atmin Pa | 1\operatorname{atm} | 101325 Pa | — Not run yet | Standard atmosphereExact by definition |
| 136 | 1 barin kPa | 1\operatorname{bar} | 100 kPa | — Not run yet | 10⁵ PaExact by definition |
| 137 | 1°in rad | 1\operatorname{deg} | 0.0174532925199 rad | — Not run yet | π/180 radExact by definition |
| 138 | 1 hin s | 1\operatorname{hour} | 3600 s | — Not run yet | 3600 sExact by definition |
| 139 | 1 kWhin MJ | 1\operatorname{kWh} | 3.6 MJ | — Not run yet | 3.6 × 10⁶ JExact by definition |
| 140 | 1 MPain N/mm² | 1\operatorname{MPa} | 1 N/mm² | — Not run yet | SI prefixesExact by definition |
| 141 | 1 tin kg | 1\operatorname{tonne} | 1000 kg | — Not run yet | Tonne (metric ton)Exact by definition |
| 142 | 1 tonin kg | 1\operatorname{ton} | 1000 kg | — Not run yet | Read as the metric tonne; the US short ton is shorttonAn AltoDocs reading rule |
| 143 | 1 nmin m | 1\operatorname{\textcolor{blue}{nm}} | 1e-9 m | — Not run yet | SI prefix nanoExact by definition |
| 144 | 1 umin m | 1\operatorname{\textcolor{blue}{um}} | 0.000001 m | — Not run yet | SI prefix microExact by definition |
| 145 | 1 mmin m | 1\operatorname{\textcolor{blue}{mm}} | 0.001 m | — Not run yet | SI prefix milliExact by definition |
| 146 | 1 cmin m | 1\operatorname{\textcolor{blue}{cm}} | 0.01 m | — Not run yet | SI prefix centiExact by definition |
| 147 | 1 dmin m | 1\operatorname{\textcolor{blue}{dm}} | 0.1 m | — Not run yet | SI prefix deciExact by definition |
| 148 | 1 min mm | 1\operatorname{\textcolor{blue}{m}} | 1000 mm | — Not run yet | SI base unit of lengthExact by definition |
| 149 | 1 kmin m | 1\operatorname{\textcolor{blue}{km}} | 1000 m | — Not run yet | SI prefix kiloExact by definition |
| 150 | 1 inchin m | 1\operatorname{\textcolor{blue}{inch}} | 0.0254 m | — Not run yet | International inch (1959)Exact by definition |
| 151 | 1 footin m | 1\operatorname{\textcolor{blue}{foot}} | 0.3048 m | — Not run yet | International foot (1959)Exact by definition |
| 152 | 1 yardin m | 1\operatorname{\textcolor{blue}{yard}} | 0.9144 m | — Not run yet | International yard (1959)Exact by definition |
| 153 | 1 milein m | 1\operatorname{\textcolor{blue}{mile}} | 1609.344 m | — Not run yet | International mileExact by definition |
| 154 | 1 hectarein m² | 1\operatorname{\textcolor{blue}{hectare}} | 10000 m² | — Not run yet | 10⁴ m²Exact by definition |
| 155 | 1 sqinin m² | 1\operatorname{\textcolor{blue}{sqin}} | 0.00064516 m² | — Not run yet | Square inchFollows from defined units |
| 156 | 1 sqftin m² | 1\operatorname{\textcolor{blue}{sqft}} | 0.09290304 m² | — Not run yet | Square footFollows from defined units |
| 157 | 1 sqydin m² | 1\operatorname{\textcolor{blue}{sqyd}} | 0.83612736 m² | — Not run yet | Square yardFollows from defined units |
| 158 | 1 sqmiin m² | 1\operatorname{\textcolor{blue}{sqmi}} | 2589988.11034 m² | — Not run yet | Square mileFollows from defined units |
| 159 | 1 acrein m² | 1\operatorname{\textcolor{blue}{acre}} | 4046.8564224 m² | — Not run yet | International acre, 43 560 ft²Follows from defined units |
| 160 | 1 litrein m³ | 1\operatorname{\textcolor{blue}{litre}} | 0.001 m³ | — Not run yet | 1 dm³Exact by definition |
| 161 | 1 mLin m³ | 1\operatorname{\textcolor{blue}{mL}} | 0.000001 m³ | — Not run yet | 1 cm³Exact by definition |
| 162 | 1 cuinin m³ | 1\operatorname{\textcolor{blue}{cuin}} | 0.000016387064 m³ | — Not run yet | Cubic inchFollows from defined units |
| 163 | 1 cuftin m³ | 1\operatorname{\textcolor{blue}{cuft}} | 0.028316846592 m³ | — Not run yet | Cubic footFollows from defined units |
| 164 | 1 cuydin m³ | 1\operatorname{\textcolor{blue}{cuyd}} | 0.764554857984 m³ | — Not run yet | Cubic yardFollows from defined units |
| 165 | 1 gallonin m³ | 1\operatorname{\textcolor{blue}{gallon}} | 0.003785411784 m³ | — Not run yet | US liquid gallon (231 in³)Exact by definition |
| 166 | 1 mgin kg | 1\operatorname{\textcolor{blue}{mg}} | 0.000001 kg | — Not run yet | SI prefix milliExact by definition |
| 167 | 1 gramin kg | 1\operatorname{\textcolor{blue}{gram}} | 0.001 kg | — Not run yet | 1/1000 kgExact by definition |
| 168 | 1 kgin gram | 1\operatorname{\textcolor{blue}{kg}} | 1000 gram | — Not run yet | SI base unit of massExact by definition |
| 169 | 1 ouncein kg | 1\operatorname{\textcolor{blue}{ounce}} | 0.028349523125 kg | — Not run yet | Avoirdupois ounce, lb/16Exact by definition |
| 170 | 1 poundin kg | 1\operatorname{\textcolor{blue}{pound}} | 0.45359237 kg | — Not run yet | Avoirdupois pound (1959)Exact by definition |
| 171 | 1 shorttonin kg | 1\operatorname{\textcolor{blue}{shortton}} | 907.18474 kg | — Not run yet | US short ton, 2000 lbExact by definition |
| 172 | 1 slugin kg | 1\operatorname{\textcolor{blue}{slug}} | 14.5939029372 kg | — Not run yet | 1 lbf·s²/ftFollows from defined units |
| 173 | 1 sin ms | 1\operatorname{\textcolor{blue}{s}} | 1000 ms | — Not run yet | SI base unit of timeExact by definition |
| 174 | 1 minin s | 1\operatorname{\textcolor{blue}{min}} | 60 s | — Not run yet | MinuteExact by definition |
| 175 | 1 hrin s | 1\operatorname{\textcolor{blue}{hr}} | 3600 s | — Not run yet | HourExact by definition |
| 176 | 1 dayin s | 1\operatorname{\textcolor{blue}{day}} | 86400 s | — Not run yet | Day, 24 hExact by definition |
| 177 | 1 weekin s | 1\operatorname{\textcolor{blue}{week}} | 604800 s | — Not run yet | Week, 7 daysExact by definition |
| 178 | 1 yearin s | 1\operatorname{\textcolor{blue}{year}} | 31557600 s | — Not run yet | Julian year, 365.25 daysAn AltoDocs reading rule |
| 179 | 1 Nin kg·m/s² | 1\operatorname{\textcolor{blue}{N}} | 1 kg·m/s² | — Not run yet | 1 kg·m/s²Exact by definition |
| 180 | 1 kNin N | 1\operatorname{\textcolor{blue}{kN}} | 1000 N | — Not run yet | SI prefix kiloExact by definition |
| 181 | 1 MNin N | 1\operatorname{\textcolor{blue}{MN}} | 1000000 N | — Not run yet | SI prefix megaExact by definition |
| 182 | 1 Pain N/m² | 1\operatorname{\textcolor{blue}{Pa}} | 1 N/m² | — Not run yet | 1 N/m²Exact by definition |
| 183 | 1 kPain Pa | 1\operatorname{\textcolor{blue}{kPa}} | 1000 Pa | — Not run yet | SI prefix kiloExact by definition |
| 184 | 1 GPain Pa | 1\operatorname{\textcolor{blue}{GPa}} | 1000000000 Pa | — Not run yet | SI prefix gigaExact by definition |
| 185 | 1 torrin Pa | 1\operatorname{\textcolor{blue}{torr}} | 133.322368421 Pa | — Not run yet | 1/760 standard atmosphereExact by definition |
| 186 | 1 Jin N·m | 1\operatorname{\textcolor{blue}{J}} | 1 N·m | — Not run yet | 1 N·mExact by definition |
| 187 | 1 kJin J | 1\operatorname{\textcolor{blue}{kJ}} | 1000 J | — Not run yet | SI prefix kiloExact by definition |
| 188 | 1 MJin J | 1\operatorname{\textcolor{blue}{MJ}} | 1000000 J | — Not run yet | SI prefix megaExact by definition |
| 189 | 1 Whin J | 1\operatorname{\textcolor{blue}{Wh}} | 3600 J | — Not run yet | 1 W × 3600 sExact by definition |
| 190 | 1 calin J | 1\operatorname{\textcolor{blue}{cal}} | 4.184 J | — Not run yet | Thermochemical calorieExact by definition |
| 191 | 1 kcalin J | 1\operatorname{\textcolor{blue}{kcal}} | 4184 J | — Not run yet | Thermochemical kilocalorieExact by definition |
| 192 | 1 BTUin J | 1\operatorname{\textcolor{blue}{BTU}} | 1055.05585262 J | — Not run yet | International Table BTUExact by definition |
| 193 | 1 Win J/s | 1\operatorname{\textcolor{blue}{W}} | 1 J/s | — Not run yet | 1 J/sExact by definition |
| 194 | 1 kWin W | 1\operatorname{\textcolor{blue}{kW}} | 1000 W | — Not run yet | SI prefix kiloExact by definition |
| 195 | 1 MWin W | 1\operatorname{\textcolor{blue}{MW}} | 1000000 W | — Not run yet | SI prefix megaExact by definition |
| 196 | 1 hpin W | 1\operatorname{\textcolor{blue}{hp}} | 745.699871582 W | — Not run yet | Mechanical horsepower, 550 ft·lbf/sFollows from defined units |
| 197 | 1 kelvinin K | 1\operatorname{\textcolor{blue}{kelvin}} | 1 K | — Not run yet | SI base unit of temperatureExact by definition |
| 198 | 1 celsiusin K | 1\operatorname{\textcolor{blue}{celsius}} | 274.15 K | — Not run yet | 1 °C is 274.15 KExact by definition |
| 199 | 1 fahrenheitin K | 1\operatorname{\textcolor{blue}{fahrenheit}} | 255.927777778 K | — Not run yet | 1 °F is (1 + 459.67) × 5/9 KExact by definition |
| 200 | 1 rankinein K | 1\operatorname{\textcolor{blue}{rankine}} | 0.555555555556 K | — Not run yet | 5/9 KExact by definition |
| 201 | 1 radin deg | 1\operatorname{\textcolor{blue}{rad}} | 57.2957795131 deg | — Not run yet | 180/π degreesExact by definition |
| 202 | 1 gradin rad | 1\operatorname{\textcolor{blue}{grad}} | 0.0157079632679 rad | — Not run yet | π/200 radExact by definition |
| 203 | 1 Hzin 1/s | 1\operatorname{\textcolor{blue}{Hz}} | 1 1/s | — Not run yet | 1 per secondExact by definition |
| 204 | 1 kHzin Hz | 1\operatorname{\textcolor{blue}{kHz}} | 1000 Hz | — Not run yet | SI prefix kiloExact by definition |
| 205 | 1 MHzin Hz | 1\operatorname{\textcolor{blue}{MHz}} | 1000000 Hz | — Not run yet | SI prefix megaExact by definition |
| 206 | 1 GHzin Hz | 1\operatorname{\textcolor{blue}{GHz}} | 1000000000 Hz | — Not run yet | SI prefix gigaExact by definition |
| 207 | 1 rpmin Hz | 1\operatorname{\textcolor{blue}{rpm}} | 0.0166666666667 Hz | — Not run yet | One revolution per minuteExact by definition |
| 208 | 1 Ain C/s | 1\operatorname{\textcolor{blue}{A}} | 1 C/s | — Not run yet | 1 C/sExact by definition |
| 209 | 1 mAin A | 1\operatorname{\textcolor{blue}{mA}} | 0.001 A | — Not run yet | SI prefix milliExact by definition |
| 210 | 1 Vin W/A | 1\operatorname{\textcolor{blue}{V}} | 1 W/A | — Not run yet | 1 W/AExact by definition |
| 211 | 1 kVin V | 1\operatorname{\textcolor{blue}{kV}} | 1000 V | — Not run yet | SI prefix kiloExact by definition |
| 212 | 1 ohmin V/A | 1\operatorname{\textcolor{blue}{ohm}} | 1 V/A | — Not run yet | 1 V/AExact by definition |
| 213 | 1 kohmin ohm | 1\operatorname{\textcolor{blue}{kohm}} | 1000 ohm | — Not run yet | SI prefix kiloExact by definition |
| 214 | 1 Mohmin ohm | 1\operatorname{\textcolor{blue}{Mohm}} | 1000000 ohm | — Not run yet | SI prefix megaExact by definition |
| 215 | 1 Fin C/V | 1\operatorname{\textcolor{blue}{F}} | 1 C/V | — Not run yet | 1 C/VExact by definition |
| 216 | 1 Cin A·s | 1\operatorname{\textcolor{blue}{C}} | 1 A·s | — Not run yet | 1 A·sExact by definition |
| 217 | 1 henryin V·s/A | 1\operatorname{\textcolor{blue}{henry}} | 1 V·s/A | — Not run yet | 1 V·s/AExact by definition |
| 218 | 1 Tin weber/m² | 1\operatorname{\textcolor{blue}{T}} | 1 weber/m² | — Not run yet | 1 Wb/m²Exact by definition |
| 219 | 1 weberin V·s | 1\operatorname{\textcolor{blue}{weber}} | 1 V·s | — Not run yet | 1 V·sExact by definition |
| 220 | 1 nmolin mol | 1\operatorname{\textcolor{blue}{nmol}} | 1e-9 mol | — Not run yet | SI prefix nanoExact by definition |
| 221 | 1 umolin mol | 1\operatorname{\textcolor{blue}{umol}} | 0.000001 mol | — Not run yet | SI prefix microExact by definition |
| 222 | 1 mmolin mol | 1\operatorname{\textcolor{blue}{mmol}} | 0.001 mol | — Not run yet | SI prefix milliExact by definition |
| 223 | 1 molin mmol | 1\operatorname{\textcolor{blue}{mol}} | 1000 mmol | — Not run yet | SI base unit of amountExact by definition |
| 224 | 1 kmolin mol | 1\operatorname{\textcolor{blue}{kmol}} | 1000 mol | — Not run yet | SI prefix kiloExact by definition |
| FunctionsEvery function in the editor’s function list, against its mathematical value. Angles in degrees carry the degree unit.55 cases, every functionNot run yet | |||||
| 225 | Equal text selects the true branchif function | if("exposed"="exposed",7,9) | 7 | — Not run yet | Exact value, written as the canvas writes it |
| 226 | Text equality does not coerce numeric-looking stringsif function | if("01"="1",7,9) | 9 | — Not run yet | Exact value, written as the canvas writes it |
| 227 | Unequal text selects the true branchif function | if("exposed"\ne"not exposed",1,0) | 1 | — Not run yet | Exact value, written as the canvas writes it |
| 228 | Program block: cover from exposure and aggregate sizeif function | @program:{"version":1,"output":"cover","statements":[{"id":"exposure-input","kind":"assign","name":"exposure","latex":"\"not exposed\""},{"id":"aggregate-input","kind":"assign","name":"a_{max}","latex":"25\\operatorname{mm}"},{"id":"exposure-if","kind":"if","branches":[{"id":"not-exposed","condition":"exposure=\"not exposed\"","statements":[{"id":"c30","kind":"assign","name":"c","latex":"30\\operatorname{mm}"}]},{"id":"exposed","condition":"exposure=\"exposed\"","statements":[{"id":"c40","kind":"assign","name":"c","latex":"40\\operatorname{mm}"}]}],"otherwise":[{"id":"c60","kind":"assign","name":"c","latex":"60\\operatorname{mm}"}]},{"id":"minimum","kind":"assign","name":"c","latex":"\\max(c,1.5\\cdot a_{max})"}],"result":"c"} | 37.5 mm | — Not run yet | Exact value, written as the canvas writes it |
| 229 | if(2 ≥ 2, 7, 9)if function | \operatorname{if}\left(2\ge 2,7,9\right) | 7 | — Not run yet | Exact value, written as the canvas writes it |
| 230 | if(2 > 2, 7, 9)if function | \operatorname{if}\left(2>2,7,9\right) | 9 | — Not run yet | Exact value, written as the canvas writes it |
| 231 | if(1 < 2, 7, missing), unused branch is not evaluatedif function | \operatorname{if}\left(1<2,7,missing\right) | 7 | — Not run yet | Exact value, written as the canvas writes it |
| 232 | √2sqrt function | \sqrt{2} | 1.41421 | — Not run yet | Exact value, written as the canvas writes it |
| 233 | √(16 m²)sqrt function | \sqrt{16\operatorname{\textcolor{blue}{m}}^{2}} | 4 m | — Not run yet | Exact value, written as the canvas writes it |
| 234 | ∛27cbrt function | \sqrt[3]{27} | 3 | — Not run yet | Exact value, written as the canvas writes it |
| 235 | ⁴√16nthRoot function | \sqrt[4]{16} | 2 | — Not run yet | Exact value, written as the canvas writes it |
| 236 | pow(2, 10)pow function | \operatorname{pow}\left(2,10\right) | 1024 | — Not run yet | Exact value, written as the canvas writes it |
| 237 | hypot(3, 4)hypot function | \operatorname{hypot}\left(3,4\right) | 5 | — Not run yet | Exact value, written as the canvas writes it |
| 238 | sin(30°)sin function | \sin\left(30\operatorname{\textcolor{blue}{deg}}\right) | 0.5 | — Not run yet | Exact value, written as the canvas writes it |
| 239 | sin(1), radianssin function | \sin\left(1\right) | 0.841471 | — Not run yet | Exact value, written as the canvas writes it |
| 240 | cos(60°)cos function | \cos\left(60\operatorname{\textcolor{blue}{deg}}\right) | 0.5 | — Not run yet | Exact value, written as the canvas writes it |
| 241 | tan(45°)tan function | \tan\left(45\operatorname{\textcolor{blue}{deg}}\right) | 1 | — Not run yet | Exact value, written as the canvas writes it |
| 242 | cot(45°)cot function | \cot\left(45\operatorname{\textcolor{blue}{deg}}\right) | 1 | — Not run yet | Exact value, written as the canvas writes it |
| 243 | sec(60°)sec function | \sec\left(60\operatorname{\textcolor{blue}{deg}}\right) | 2 | — Not run yet | Exact value, written as the canvas writes it |
| 244 | csc(30°)csc function | \csc\left(30\operatorname{\textcolor{blue}{deg}}\right) | 2 | — Not run yet | Exact value, written as the canvas writes it |
| 245 | arcsin(0.5)arcsin function | \arcsin\left(0.5\right) | 0.523599 | — Not run yet | Exact value, written as the canvas writes it |
| 246 | arccos(0.5)arccos function | \arccos\left(0.5\right) | 1.0472 | — Not run yet | Exact value, written as the canvas writes it |
| 247 | arctan(1)arctan function | \arctan\left(1\right) | 0.785398 | — Not run yet | Exact value, written as the canvas writes it |
| 248 | asin(0.5)asin function | \operatorname{asin}\left(0.5\right) | 0.523599 | — Not run yet | Exact value, written as the canvas writes it |
| 249 | acos(0.5)acos function | \operatorname{acos}\left(0.5\right) | 1.0472 | — Not run yet | Exact value, written as the canvas writes it |
| 250 | atan(1)atan function | \operatorname{atan}\left(1\right) | 0.785398 | — Not run yet | Exact value, written as the canvas writes it |
| 251 | atan2(1, −1)atan2 function | \operatorname{atan2}\left(1,-1\right) | 2.35619 | — Not run yet | Exact value, written as the canvas writes it |
| 252 | sinh(1)sinh function | \sinh\left(1\right) | 1.1752 | — Not run yet | Exact value, written as the canvas writes it |
| 253 | cosh(1)cosh function | \cosh\left(1\right) | 1.54308 | — Not run yet | Exact value, written as the canvas writes it |
| 254 | tanh(1)tanh function | \tanh\left(1\right) | 0.761594 | — Not run yet | Exact value, written as the canvas writes it |
| 255 | asinh(1)asinh function | \operatorname{asinh}\left(1\right) | 0.881374 | — Not run yet | Exact value, written as the canvas writes it |
| 256 | acosh(2)acosh function | \operatorname{acosh}\left(2\right) | 1.31696 | — Not run yet | Exact value, written as the canvas writes it |
| 257 | atanh(0.5)atanh function | \operatorname{atanh}\left(0.5\right) | 0.549306 | — Not run yet | Exact value, written as the canvas writes it |
| 258 | log₂(8)log function | \log_{2}\left(8\right) | 3 | — Not run yet | Exact value, written as the canvas writes it |
| 259 | log₁₀(1000)log10 function | \log_{10}\left(1000\right) | 3 | — Not run yet | Exact value, written as the canvas writes it |
| 260 | log2(32)log2 function | \operatorname{log2}\left(32\right) | 5 | — Not run yet | Exact value, written as the canvas writes it |
| 261 | ln(10)ln function | \ln\left(10\right) | 2.30259 | — Not run yet | Exact value, written as the canvas writes it |
| 262 | exp(1)exp function | \exp\left(1\right) | 2.71828 | — Not run yet | Exact value, written as the canvas writes it |
| 263 | |−3.5 kN|abs function | \left|-3.5\operatorname{\textcolor{blue}{kN}}\right| | 3.5 kN | — Not run yet | Exact value, written as the canvas writes it |
| 264 | sign(−2)sign function | \operatorname{sign}\left(-2\right) | -1 | — Not run yet | Exact value, written as the canvas writes it |
| 265 | floor(2.7)floor function | \operatorname{floor}\left(2.7\right) | 2 | — Not run yet | Exact value, written as the canvas writes it |
| 266 | ceil(2.1)ceil function | \operatorname{ceil}\left(2.1\right) | 3 | — Not run yet | Exact value, written as the canvas writes it |
| 267 | round(2.5)round function | \operatorname{round}\left(2.5\right) | 3 | — Not run yet | Exact value, written as the canvas writes it |
| 268 | round(3.14159, 2)round function | \operatorname{round}\left(3.14159,2\right) | 3.14 | — Not run yet | Exact value, written as the canvas writes it |
| 269 | fix(−2.7)fix function | \operatorname{fix}\left(-2.7\right) | -2 | — Not run yet | Exact value, written as the canvas writes it |
| 270 | max(3 kN, 2500 N)max function | \max\left(3\operatorname{\textcolor{blue}{kN}},2500\operatorname{\textcolor{blue}{N}}\right) | 3 kN | — Not run yet | Exact value, written as the canvas writes it |
| 271 | min(3, 7, 5)min function | \min\left(3,7,5\right) | 3 | — Not run yet | Exact value, written as the canvas writes it |
| 272 | sum(1, 2, 3, 4)sum function | \operatorname{sum}\left(1,2,3,4\right) | 10 | — Not run yet | Exact value, written as the canvas writes it |
| 273 | prod(2, 3, 4)prod function | \operatorname{prod}\left(2,3,4\right) | 24 | — Not run yet | Exact value, written as the canvas writes it |
| 274 | mean(2, 4, 9)mean function | \operatorname{mean}\left(2,4,9\right) | 5 | — Not run yet | Exact value, written as the canvas writes it |
| 275 | median(3, 1, 4, 1, 5)median function | \operatorname{median}\left(3,1,4,1,5\right) | 3 | — Not run yet | Exact value, written as the canvas writes it |
| 276 | std(2, 4, 4, 4, 5, 5, 7, 9)std function | \operatorname{std}\left(2,4,4,4,5,5,7,9\right) | 2.13809 | — Not run yet | Exact value, written as the canvas writes it |
| 277 | mod(17, 5)mod function | \operatorname{mod}\left(17,5\right) | 2 | — Not run yet | Exact value, written as the canvas writes it |
| 278 | gcd(12, 18)gcd function | \operatorname{gcd}\left(12,18\right) | 6 | — Not run yet | Exact value, written as the canvas writes it |
| 279 | lcm(4, 6)lcm function | \operatorname{lcm}\left(4,6\right) | 12 | — Not run yet | Exact value, written as the canvas writes it |
| Displayed resultsWhat the canvas shows: rounding, number formats, and the unit each kind of result is shown in.35 display rulesNot run yet | |||||
| 280 | Conditional pass message | \operatorname{if}\left(500\operatorname{mm}^{2}\ge4\operatorname{cm}^{2},\text{"Min steel OK"},\text{"Steel Inadequate"}\right) | \text{``Min steel OK''} | — Not run yet | 2 decimals |
| 281 | Conditional failure message | if(300<200,"OK","NOT - OK") | \text{``NOT - OK''} | — Not run yet | 2 decimals |
| 282 | Numeric-looking text remains text | if(1=1,"123","456") | \text{``123''} | — Not run yet | 2 decimals |
| 283 | Quoted message punctuation is escaped | if(1\ne2,"50% & safe","fail") | \text{``50\% \& safe''} | — Not run yet | 2 decimals |
| 284 | Two decimals | \frac{1}{3} | 0.33 | — Not run yet | 2 decimals |
| 285 | A half rounds away from zero | 0.125 | 0.13 | — Not run yet | 2 decimals |
| 286 | Rounded as written, not as stored in binary | 2.675 | 2.68 | — Not run yet | 2 decimals |
| 287 | Negative values round the same way | -2.675 | -2.68 | — Not run yet | 2 decimals |
| 288 | Percentage | 0.285 | 29\% | — Not run yet | 0 decimals, percentage |
| 289 | Engineering notation | 12345 | 12.35 \cdot 10^{3} | — Not run yet | 2 decimals, engineering |
| 290 | A small value never shows as zero | 0.000012 | 0.000012 | — Not run yet | 2 decimals |
| 291 | Zero shows as zero | 0 | 0.00 | — Not run yet | 2 decimals |
| 292 | A small area in m² keeps its digits | 1570\operatorname{\textcolor{blue}{mm}}^{2} | 0.00157 \operatorname{\textcolor{blue}{m}}^{2} | — Not run yet | 2 decimals, shown in m² |
| 293 | Force in kN | 1500\operatorname{\textcolor{blue}{N}} | 1.50 \operatorname{\textcolor{blue}{kN}} | — Not run yet | 2 decimals |
| 294 | Force: from 1000 N in kN | 1000\operatorname{\textcolor{blue}{N}} | 1.00 \operatorname{\textcolor{blue}{kN}} | — Not run yet | 2 decimals |
| 295 | Force: below 1000 N in N | 999\operatorname{\textcolor{blue}{N}} | 999.00 \operatorname{\textcolor{blue}{N}} | — Not run yet | 2 decimals |
| 296 | Moment: below 1000 N·m in N·m | 999\operatorname{\textcolor{blue}{N}}\cdot\operatorname{\textcolor{blue}{m}} | 999.00 \operatorname{\textcolor{blue}{N}} \cdot \operatorname{\textcolor{blue}{m}} | — Not run yet | 2 decimals |
| 297 | Line load in kN/m | \frac{5\operatorname{\textcolor{blue}{kN}}}{2\operatorname{\textcolor{blue}{m}}} | 2.50 \frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}} | — Not run yet | 2 decimals |
| 298 | Unit weight in kN/m³ | 25\frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}^{3}} | 25.00 \frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}^{3}} | — Not run yet | 2 decimals |
| 299 | Bending stiffness in kN·m² | 210\operatorname{\textcolor{blue}{GPa}}\cdot 8356\operatorname{\textcolor{blue}{cm}}^{4} | 17547.6 \operatorname{\textcolor{blue}{kN}} \cdot \operatorname{\textcolor{blue}{m}}^{2} | — Not run yet | 1 decimals |
| 300 | Stress: from 1 MPa in MPa | 1000000\operatorname{\textcolor{blue}{Pa}} | 1.00 \operatorname{\textcolor{blue}{MPa}} | — Not run yet | 2 decimals |
| 301 | Modulus: from 1 GPa in GPa | 1000000000\operatorname{\textcolor{blue}{Pa}} | 1.00 \operatorname{\textcolor{blue}{GPa}} | — Not run yet | 2 decimals |
| 302 | Moment in kN·m | 5\operatorname{\textcolor{blue}{kN}}\cdot 2\operatorname{\textcolor{blue}{m}} | 10.00 \operatorname{\textcolor{blue}{kN}} \cdot \operatorname{\textcolor{blue}{m}} | — Not run yet | 2 decimals |
| 303 | Stress in MPa | 235\frac{\operatorname{\textcolor{blue}{N}}}{\operatorname{\textcolor{blue}{mm}}^{2}} | 235.0 \operatorname{\textcolor{blue}{MPa}} | — Not run yet | 1 decimals |
| 304 | Surface load in kN/m² | 2500\operatorname{\textcolor{blue}{Pa}} | 2.50 \frac{\operatorname{\textcolor{blue}{kN}}}{\operatorname{\textcolor{blue}{m}}^{2}} | — Not run yet | 2 decimals |
| 305 | Imperial worksheet: force in kip | 1500\operatorname{\textcolor{blue}{lbf}} | 1.50 \operatorname{\textcolor{blue}{kip}} | — Not run yet | 2 decimals, US units |
| 306 | Imperial worksheet: from 1000 lbf in kip | 1000\operatorname{\textcolor{blue}{lbf}} | 1.00 \operatorname{\textcolor{blue}{kip}} | — Not run yet | 2 decimals, US units |
| 307 | Imperial worksheet: below 1000 lbf in lbf | 999\operatorname{\textcolor{blue}{lbf}} | 999.00 \operatorname{\textcolor{blue}{lbf}} | — Not run yet | 2 decimals, US units |
| 308 | Imperial worksheet: line load in kip/ft | \frac{1200\operatorname{\textcolor{blue}{lbf}}}{\operatorname{\textcolor{blue}{foot}}} | 1.20 \frac{\operatorname{\textcolor{blue}{kip}}}{\operatorname{\textcolor{blue}{ft}}} | — Not run yet | 2 decimals, US units |
| 309 | A unit you choose is kept | 54\operatorname{\textcolor{blue}{kN}}\cdot\operatorname{\textcolor{blue}{m}} | 39.83 \operatorname{\textcolor{blue}{kip}} \cdot \operatorname{\textcolor{blue}{ft}} | — Not run yet | 2 decimals, shown in kip·ft |
| 310 | Temperature units take no prefix | 12\cdot 10^{-6}\frac{1}{\operatorname{\textcolor{blue}{K}}} | 0.000012 \operatorname{\textcolor{blue}{K}}^{-1} | — Not run yet | 2 decimals |
| 311 | Mixed units add exactly | 1\operatorname{\textcolor{blue}{m}}+1\operatorname{\textcolor{blue}{foot}} | 1.305 \operatorname{\textcolor{blue}{m}} | — Not run yet | 3 decimals |
| 312 | Lengths keep the unit they were written in | 3\operatorname{\textcolor{blue}{foot}}+2\operatorname{\textcolor{blue}{foot}} | 5.00 \operatorname{\textcolor{blue}{foot}} | — Not run yet | 2 decimals |
| 313 | An area elsewhere does not change how m² is shown | 2.5\operatorname{\textcolor{blue}{m}}^{2} | 2.50 \operatorname{\textcolor{blue}{m}}^{2} | — Not run yet | 2 decimals |
| 314 | A rounded display keeps the full value | a = 1/3, shown as 0.33, then 3 · a | 1 | — Not run yet | Rounding touches the display only, never the stored value |
| Calculated as drawnThe drawn structure decides the value, with 9 definitions: q = 12 kN/m, L = 6 m, x = 4, a = 2 and b = 3.14 casesNot run yet | |||||
| 315 | ⅛ · q · L² | \frac{1}{8}\cdot q\cdot L^{2} | 54 kN·m | — Not run yet | What the page shows is what is calculated |
| 316 | (q/2) · L | \frac{q}{2}\cdot L | 36 kN | — Not run yet | What the page shows is what is calculated |
| 317 | (6/2) · x | \frac{6}{2}\cdot x | 12 | — Not run yet | What the page shows is what is calculated |
| 318 | (a/b)² | \frac{a}{b}^{2} | 0.444444 | — Not run yet | What the page shows is what is calculated |
| 319 | −½ · x | -\frac{1}{2}\cdot x | -2 | — Not run yet | What the page shows is what is calculated |
| 320 | x · ½ | x\cdot\frac{1}{2} | 2 | — Not run yet | What the page shows is what is calculated |
| 321 | a over (b/x) | \frac{a}{\frac{b}{x}} | 2.66667 | — Not run yet | What the page shows is what is calculated |
| 322 | sin(π/2) | \sin\frac{\operatorname{\pi}}{2} | 1 | — Not run yet | What the page shows is what is calculated |
| 323 | 0.1 + 0.2 | 0.1+0.2 | 0.3 | — Not run yet | What the page shows is what is calculated |
| 324 | 5 N/mm² | 5\frac{\operatorname{N}}{\operatorname{mm}^{2}} | 5 MPa | — Not run yet | What the page shows is what is calculated |
| 325 | Bar′ (Bar′ := 5 after Bar := 2) | Bar' | 5 | — Not run yet | What the page shows is what is calculated |
| 326 | A′_bar written with the prime after the subscript | A_{bar}^{\prime} | 700 mm² | — Not run yet | What the page shows is what is calculated |
| 327 | Rebar₁, a combo box row (30M) read by index | Rebar_{1} | 700 mm² | — Not run yet | What the page shows is what is calculated |
| 328 | Rebar₂ / 2, the diameter column of the same row | \frac{Rebar_{2}}{2} | 14.95 mm | — Not run yet | What the page shows is what is calculated |
| Refused when unclearA formula that could mean two things, or uses a slash, gets no answer and a reason. Never a guess.13 casesNot run yet | |||||
| 329 | 5 kN / 2 m | 5\operatorname{\textcolor{blue}{kN}}/2\operatorname{\textcolor{blue}{m}} | No answer | — Not run yet | 5 kN ÷ (2 m), or (5 kN ÷ 2) · m? The slash does not show which.Write instead: A fraction: 5 kN over 2 m |
| 330 | q · L²/8 | q\cdot L^{2}/8 | No answer | — Not run yet | Here both readings agree, but a slash never shows what it divides. MathCanvas divides only with a drawn fraction.Write instead: A fraction: q · L² over 8 |
| 331 | 12 kN/m | 12\operatorname{\textcolor{blue}{kN}}/\operatorname{\textcolor{blue}{m}} | No answer | — Not run yet | A slash pasted or sent as text. The unit list writes kN/m as a fraction.Write instead: kN/m from the unit list |
| 332 | ⅛q · L² | \frac{1}{8}q\cdot L^{2} | No answer | — Not run yet | A fraction touching a letter. MathCanvas always shows the multiplication dot next to a fraction, so every product is visible.Write instead: ⅛ · q · L² |
| 333 | 2 ½ | 2\frac{1}{2} | No answer | — Not run yet | Two and a half, or two times a half?Write instead: 2 + ½ or 2 · ½ |
| 334 | 5%x | 5\%x | No answer | — Not run yet | 5 % of x, or 5 modulo x?Write instead: 5 % · x |
| 335 | log(100) | \log\left(100\right) | No answer | — Not run yet | Base 10 or base e? Tools differ.Write instead: log₁₀(100) or ln(100) |
| 336 | x(a + b) | x\left(a+b\right) | No answer | — Not run yet | A function x of a + b, or x times (a + b)?Write instead: x · (a + b) |
| 337 | 3 × 4 | 3\times 4 | No answer | — Not run yet | × also means the cross product.Write instead: 3 · 4 |
| 338 | 6 ÷ 3 | 6\div 3 | No answer | — Not run yet | ÷ is written in some places for ratios and ranges.Write instead: A fraction: 6 over 3 |
| 339 | ± 3 | \pm 3 | No answer | — Not run yet | Two values in one result.Write instead: One region per case |
| 340 | ∓ 3 | \mp 3 | No answer | — Not run yet | Two values in one result.Write instead: One region per case |
| 341 | 5′ | 5' | No answer | — Not run yet | A prime marks a name, as in A′. After a number it could mean feet or a transpose.Write instead: A name such as d′, or 5 ft |
| Working gives the resultEach formula’s working, with the numbers filled in, must give the result again.14 casesNot run yet | |||||
| 342 | E_d = 1.35·G_k + 1.5·Q_k | The numbers, filled in | 21 kN/m | — Not run yet | The working, evaluated again by the engine |
| 343 | g = ρ·h | The numbers, filled in | 5 kN/m² | — Not run yet | The working, evaluated again by the engine |
| 344 | s = μ₁·C_e·C_t·s_k | The numbers, filled in | 0.8 kN/m² | — Not run yet | The working, evaluated again by the engine |
| 345 | ΔL = α·ΔT·L | The numbers, filled in | 3.6 mm | — Not run yet | The working, evaluated again by the engine |
| 346 | M = qL²/8 | The numbers, filled in | 54 kN·m | — Not run yet | The working, evaluated again by the engine |
| 347 | V = qL/2 | The numbers, filled in | 36 kN | — Not run yet | The working, evaluated again by the engine |
| 348 | δ = 5qL⁴/(384EI) | The numbers, filled in | 11.54 mm | — Not run yet | The working, evaluated again by the engine |
| 349 | M_c,Rd = W_pl·f_y/γ_M0 | The numbers, filled in | 147.674 kN·m | — Not run yet | The working, evaluated again by the engine |
| 350 | η = M_Ed/M_c,Rd | The numbers, filled in | 0.36567 | — Not run yet | The working, evaluated again by the engine |
| 351 | F_v,Rd = α_v·f_ub·A_s/γ_M2 | The numbers, filled in | 94.08 kN | — Not run yet | The working, evaluated again by the engine |
| 352 | f_cd = α_cc·f_ck/γ_c | The numbers, filled in | 20 MPa | — Not run yet | The working, evaluated again by the engine |
| 353 | μ = M_Ed/(b·d²·f_cd) | The numbers, filled in | 0.0987654 | — Not run yet | The working, evaluated again by the engine |
| 354 | N_cr = π²EI/L_cr² | The numbers, filled in | 4810.77 kN | — Not run yet | The working, evaluated again by the engine |
| 355 | M = wL²/8 | The numbers, filled in | 60 kip·ft | — Not run yet | The working, evaluated again by the engine |
| Random formulasBuilt by the computer from a fixed starting point, so every run checks exactly the same formulas, to catch mistakes no one thought to test.3,000 formulasNot run yet | |||||
| 356 | Written outseed 20261030 | Every product as ·, every grouping bracketed | Each its own value, worked out separately | — Not run yet | Seeded: the same formulas every run |
| 357 | Everyday notationseed 17 | A fraction followed by a name, as an engineer types it | The right value, or refused with a reason | — Not run yet | Seeded: the same formulas every run |
Two more checks run before every release but not in your browser: a second calculator, written separately in Python, recomputes every answer above, and the 32 worksheets that ship with AltoDocs (360 results) must give their recorded results.
For engineers and reviewers
How MathCanvas calculates
You write the formula.
The MathLive editor stores what you see as LaTeX, so the stored formula has the same structure as the one on screen.
MathCanvas reads it into one tree.
Fractions, powers, units and names become a single expression tree, written out with every bracket explicit:
\frac{1}{8}\cdot q\cdot L^{2}becomes((1 / 8) * q) * (L ^ 2). Notation with a second reading is refused here.mathjs computes it.
The open-source mathjs library evaluates the tree with 64-significant-digit decimal arithmetic and its unit system, so 0.1 + 0.2 is exactly 0.3 and N/mm² converts to MPa.
One engine everywhere.
MathCanvas, the AltoDocs API and the tools AI assistants use evaluate through the same engine, so a worksheet gives the same answer wherever it is calculated.
Each check states how independent its reference is: recomputed outside the engine (a second implementation), printed by a third party (worked examples), or fixed by definition (units). An independent review of the method is the remaining step.
Every result shows its working
Checking engineers verify a calculation line by line. MathCanvas shows each result the same way: the formula as the engine reads it, then the same formula with the values it used, then the result. Open the variable inspector on any finished region to see it; the PDF can print it as an appendix, and the API and AI tools return it with every result.
M_Ed = 1 / 8 * q * L ^ 2 = 1 / 8 * (12 kN / m) * (6 m) ^ 2 = 54 kN m
The working is checked too: evaluating each benchmark’s substituted line, with its displayed values, must give the result again — the last group of rows in the table above.
Formulas no one wrote by hand
The computer builds 3,000 formulas from a fixed starting point (seed), so every run checks exactly the same ones. Half are written out with every bracket and multiplication sign; each must give the value computed for it separately. The other half use everyday notation, such as a fraction followed by a name; each must give the right value or be refused with a reason, and fewer than a quarter may be refused.
Formulas no one wrote by hand catch mistakes no one thought to test: many of the misreadings fixed in engine 2 showed up this way.
Sources
Where the answers come from
Each row of the table says which source its expected answer rests on. The sources themselves:
- JRC EUR 27346 EN (2015)M. Veljkovic et al. (eds.), Eurocodes: Background & Applications. Design of Steel Buildings. Worked examples. JRC Science and Policy Report EUR 27346 EN, Publications Office of the European Union, 2015. ISBN 978-92-79-49573-1, doi:10.2788/605700.
- JRC EUR 26566 EN (2014)F. Biasioli, M. Poljanšek, B. Nikolova, S. Dimova, A. Pinto (eds.), Eurocode 2: Background & Applications. Design of Concrete Buildings. Worked examples. JRC Scientific and Policy Report EUR 26566 EN, Publications Office of the European Union, 2014. ISBN 978-92-79-36548-5, doi:10.2788/35386.
- JRC EUR 26698 EN (2014)M. Poljanšek, B. Nikolova, L. Sousa, S. Dimova, A. Pinto (eds.), Eurocodes: Background & Applications. Structural Fire Design. Worked examples. JRC Science and Policy Report EUR 26698 EN, Publications Office of the European Union, 2014. ISBN 978-92-79-38671-8, doi:10.2788/85432.
- NIST StRDNIST Statistical Reference Datasets, Univariate Summary Statistics: datasets NumAcc1 and Mavro with certified values. National Institute of Standards and Technology, Information Technology Laboratory.
- NIST SP 811 (2008)A. Thompson and B. N. Taylor, Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 edition, Appendix B.
The second calculator, in Python
This script shares no code with the engine: plain Python, with inputs typed in by hand. It recomputes every benchmark, published answer and function above, and our test suite checks that it agrees. Copy it and run it with any Python 3. Python is only the measuring tool here; the Python cells in MathCanvas are a separate feature.
"""Independent recomputation of the AltoDocs validation references.
A second implementation in another language, sharing no code with the
calculation engine: plain Python floats, inputs typed in by hand from the
cases on altodocs.io/verification. Run it with any Python 3:
python3 references.py
It prints every reference in the order the validation page lists them, in
the units shown there. The engine's test suite runs this script and checks
that it agrees with the published case data.
"""
import json
from decimal import ROUND_HALF_UP, Decimal
from math import (acos, acosh, asin, asinh, atan, atan2, atanh, ceil, cos, cosh, exp, floor, gcd, hypot,
lcm, log, log2, log10, pi, radians, sin, sinh, sqrt, tan, tanh, trunc)
from statistics import mean, median, stdev
kN, m, mm, cm, MPa, GPa = 1e3, 1.0, 1e-3, 1e-2, 1e6, 1e9 # SI: N, m, Pa
SQRT3 = sqrt(3)
# Engineering benchmarks, in each check's unit, in the order of the cases.
q, L, E, I = 12 * kN / m, 6 * m, 210 * GPa, 8356 * cm**4
W_pl, f_y = 628.4 * cm**3, 235 * MPa
M_c_Rd = W_pl * f_y / 1.0
benchmarks = [
(1.35 * 10 + 1.5 * 5), # E_d [kN/m]
25 * 0.2, # g = ρh [kN/m²]
0.8 * 1.0 * 1.0 * 1.0, # s = μ₁ C_e C_t s_k [kN/m²]
12e-6 * 30 * 10 * m / mm, # ΔL = α ΔT L [mm]
q * L**2 / 8 / (kN * m), # M = qL²/8 [kN m]
q * L / 2 / kN, # V = qL/2 [kN]
5 * q * L**4 / (384 * E * I) / mm, # δ = 5qL⁴/(384EI) [mm]
M_c_Rd / (kN * m), # M_c,Rd = W_pl f_y / γ_M0 [kN m]
54 * kN * m / M_c_Rd, # η = M_Ed / M_c,Rd [-]
0.6 * 800 * MPa * 245 * mm**2 / 1.25 / kN, # F_v,Rd [kN]
1.0 * 30 * MPa / 1.5 / MPa, # f_cd = α_cc f_ck / γ_c [MPa]
120 * kN * m / (300 * mm * (450 * mm) ** 2 * (20 * MPa)), # μ [-]
pi**2 * E * I / (6 * m) ** 2 / kN, # N_cr = π²EI/L_cr² [kN]
1.2 * 20**2 / 8, # M = wL²/8 [kip ft]
]
# NIST StRD datasets, as published (NumAcc1.dat and Mavro.dat, data lines). The
# Mavro values are decimal, so they are read as decimals: in binary floats the
# certified standard deviation is only reproduced to 13 digits.
NUMACC1 = [10000001, 10000003, 10000002]
MAVRO = [Decimal(v) for v in '''
2.00180 2.00170 2.00180 2.00190 2.00180 2.00170 2.00150 2.00140 2.00150 2.00150
2.00170 2.00180 2.00180 2.00190 2.00190 2.00210 2.00200 2.00160 2.00140 2.00130
2.00130 2.00150 2.00150 2.00160 2.00150 2.00140 2.00130 2.00140 2.00150 2.00140
2.00150 2.00160 2.00150 2.00160 2.00190 2.00200 2.00200 2.00210 2.00220 2.00230
2.00240 2.00250 2.00270 2.00260 2.00260 2.00260 2.00270 2.00260 2.00250 2.00240
'''.split()]
# Published results, from the printed inputs: JRC EUR 27346 EN (steel),
# JRC EUR 26566 EN (concrete), JRC EUR 26698 EN (fire), NIST StRD (statistics).
published = [
170.9 * cm**2 * 355 * MPa / 1.00 / kN, # N_c,Rd [kN]
pi * sqrt(210 * GPa / (355 * MPa)), # λ₁
4.335 * m / (7.53 * cm), # λ_z
57.57 / 76.41, # λ̄_z
0.5 * (1 + 0.49 * (0.75 - 0.2) + 0.75**2), # Φ_z
1 / (0.92 + sqrt(0.92**2 - 0.75**2)), # χ_z
0.69 * 170.9 * cm**2 * 355 * MPa / 1.00 / kN, # N_b,Rd [kN]
1307 * cm**3 * 355 * MPa / 1.00 / (kN * m), # M_c,Rd [kN m]
42.69 * cm**2 * 355 * MPa / (SQRT3 * 1.00) / kN, # V_pl,Rd [kN]
sqrt(1307 * cm**3 * 355 * MPa / (164.7 * kN * m)), # λ̄_LT
0.5 * (1 + 0.34 * (1.68 - 0.2) + 1.68**2), # Φ_LT
1 / (2.16 + sqrt(2.16**2 - 1.68**2)), # χ_LT
0.28 * 1307 * cm**3 * 355 * MPa / 1.00 / (kN * m), # M_b,Rd [kN m]
6.2 * mm * 130 * mm * 235 * MPa / (SQRT3 * 1.00) / kN, # V_pl,Rd beam web [kN]
0.6 * 157 * mm**2 * 400 * MPa / 1.25 / kN, # F_v,Rd M16 [kN]
2 * 3 * mm * 130 * mm * 360 * MPa / (SQRT3 * 0.8 * 1.25) / kN, # F_w,Rd [kN]
0.6 * 245 * mm**2 * 500 * MPa / 1.25 / kN, # F_v,Rd M20 [kN]
2.5 * 0.659 * 20 * mm * 5.6 * mm * 360 * MPa / 1.25 / kN, # F_b,Rd beam web [kN]
(0.5 * 290 * mm**2 * 360 * MPa / 1.25 + 670 * mm**2 * 235 * MPa / (SQRT3 * 1.00)) / kN, # V_eff,2,Rd fin plate [kN]
10 * mm * 140 * mm * 235 * MPa / (SQRT3 * 1.00) / kN, # V_pl,Rd fin plate [kN]
(0.5 * 162.4 * mm**2 * 360 * MPa / 1.25 + 515.2 * mm**2 * 235 * MPa / (SQRT3 * 1.00)) / kN, # V_eff,2,Rd beam web [kN]
(10 * mm * (140 * mm) ** 2 / 6) * 235 * MPa / 1.00 / (kN * m), # M_el,Rd [kN m]
# JRC EUR 26566 EN, concrete (lengths in mm, stresses in N/mm²).
0.2 * 2875 + 0.1 * (0.85 * 7125), # b_eff,1 mid-span [mm]
2 * (0.2 * 2875 + 0.1 * 0.85 * 7125) + 250, # b_eff mid-span [mm]
0.2 * 2875 + 0.1 * (0.30 * 7125), # b_eff,1 support [mm]
2 * 788.8 + 250, # b_eff support [mm]
89.3e6 / (2611.2 * 372**2 * (25 / 1.5)), # K mid-span
0.5 * (1 + sqrt(1 - 2 * 0.0148)), # z/d mid-span
89.3e6 / (435 * 372 * 0.9925), # A_sl mid-span [mm²]
132.9e6 / (250 * 372**2 * (25 / 1.5)), # K support
0.5 * (1 + sqrt(1 - 2 * 0.230)), # z/d support
132.9e6 / (435 * 372 * 0.867), # A_sl support [mm²]
4 * pi * 14**2 / 4, # A_s 4ϕ14 [mm²]
9 * pi * 12**2 / 4, # A_s 9ϕ12 [mm²]
129.9 * (3.36 - 0.372) / 3.36, # V_Ed,red [kN]
1 + sqrt(200 / 372), # k
565 / (250 * 372), # ρ_l
0.12 * (1 + sqrt(200 / 372)) * (100 * 565 / (250 * 372) * 25) ** (1 / 3) * 250 * 372 / 1e3, # V_Rd,c [kN]
115.52e3 / (0.9 * 372 * 435 * 2.5) * 1e3, # A_sw/s [mm²/m]
0.08 * sqrt(25) / 500 * 250 * 1e3, # a_sw,min [mm²/m]
0.6 * (1 - 25 / 250), # ν
250 * 0.9 * 372 * 0.54 * (25 / 1.5) / (2.5 + 0.4) / 1e3, # V_Rd,max [kN]
1.0 * 1.8 / 1.5, # f_ctd [N/mm²]
0.5 * (2611.2 - 250) / 2611.2 * 115520 / (0.9 * 372 * 180), # ν_Ed,A [N/mm²]
0.5 * (2611.2 - 250) / 2611.2 * 89830 / (0.9 * 372 * 180), # ν_Ed,C [N/mm²]
0.5 * (1827.6 - 250) / 1827.6 * 101830 / (0.9 * 372 * 180), # ν_Ed,B,left [N/mm²]
0.5 * (1827.6 - 250) / 1827.6 * 131410 / (0.9 * 372 * 180), # ν_Ed,B,right [N/mm²]
0.5 * (2611.2 - 250) / 2611.2 * 115520 / (0.9 * 372 * 435) / 2.0, # A_st/s support A [mm²/mm]
0.5 * (2611.2 - 250) / 2611.2 * 89830 / (0.9 * 372 * 435) / 2.0, # A_st/s support C [mm²/mm]
0.5 * (1827.6 - 250) / 1827.6 * 101830 / (0.9 * 372 * 435) / 2.0, # A_st/s support B left [mm²/mm]
0.5 * (1827.6 - 250) / 1827.6 * 131410 / (0.9 * 372 * 435) / 2.0, # A_st/s support B right [mm²/mm]
pi * 8**2 / (4 * 250), # ϕ8/250 [mm²/mm]
1.3 * (4.5 + 3.0), # G_Ed [kN/m²]
1.3 * (4.5 + 3.0) + 1.5 * 2.0, # L_Ed [kN/m²]
210 - 30 - 16 / 2, # d_y [mm]
210 - 30 - 16 - 16 / 2, # d_z [mm]
0.4 * 0.54 * 25 / 1.5, # ν_Rd,max [N/mm²]
1.15 * 705e3 / (4 * 500 * 164), # ν_Ed at u₀ [N/mm²]
4 * 500 + 2 * pi * 2 * 164, # u₁ [mm]
1.15 * 705e3 / (4061 * 164), # ν_Ed at u₁ [N/mm²]
1 + sqrt(200 / 164), # k punching
0.12 * 2.0 * (100 * 0.0083 * 25) ** (1 / 3), # ν_Rd,c [N/mm²]
0.035 * 2.0**1.5 * 25**0.5, # ν_min [N/mm²]
(1.22 - 0.75 * 0.66) * 4060.88 * 123 / (1.5 * 291), # A_sw per perimeter [mm²]
1.15 * 705e3 / (0.66 * 164), # u_out [mm]
(7490.30 - 4 * 500) / (2 * pi), # a [mm]
# JRC EUR 26698 EN, fire: steel beam and column (B. Zhao), timber (A. Frangi).
1.25 * 23.135 * 7, # P_fi,d,t [kN]
1.12 * 3**2 / 2 + 202.4 * 3 / 2, # M_fi,d,t [kN m]
0.85 * sqrt(235 / 275), # ε
72 * 0.85 * sqrt(235 / 275), # 72ε
9 * 0.85 * sqrt(235 / 275), # 9ε
2088.47e3 * 275 / 1.0 / 1e6, # M_pl,Rd [kN m]
4896 * 275 / sqrt(3) / 1.0 / 1e3, # V_pl,Rd [kN]
308.6 * 1.0 / (574.3 * 1.0), # μ₀,M
104.5 * 1.0 / (777.3 * 1.0), # μ₀,V
0.537 * 0.7 * 1.0, # μ₀,M,κ unprotected
max(0.376, 0.134), # μ₀ unprotected
39.19 * log(1 / (0.9674 * 0.376**3.833) - 1) + 482, # θ_cr unprotected [°C]
600 + (0.47 - 0.376) / (0.47 - 0.23) * 100, # θ_cr from k_y,θ [°C]
0.9 * 70 / 107, # k_sh
0.589 / (600 * 7850) * 107 * 3, # k_sh (A_m/V) Δt / (c_a ρ_a)
308.6 / 574.3 * 0.85 * 1.0, # μ₀,M,κ protected
39.19 * log(1 / (0.9674 * 0.457**3.833) - 1) + 482, # θ_cr protected [°C]
1200 * 350 / (600 * 7850) * 10e-3 * 107, # ϕ sprayed protection
14.105 * 7 + 202.4 + 1.12 * 6, # P_fi,d,t column [kN]
120 - 2 * (30 * 0.8 + 7), # b_fi secondary beam [mm]
260 - (30 * 0.8 + 7), # h_fi secondary beam [mm]
58 * 229**2 / 6 / 1e3, # W_fi secondary beam [cm³]
(0.17 + 0.09 + 1.32 + 0.06 + 0.28 + 1.0 + 0.3 * 2.0) * 1.0 * 4.0**2 / 8, # M_d,fi secondary [kN m]
(0.17 + 0.09 + 1.32 + 0.06 + 0.28 + 1.0 + 0.3 * 2.0) * 1.0 * 4.0**2 / 8 * 1e6 / (58 * 229**2 / 6), # σ_d,fi secondary [N/mm²]
160 - 2 * (30 * 0.7 + 7), # b_fi main beam [mm]
735 - (30 * 0.7 + 7), # h_fi main beam [mm]
104 * 707**2 / 6 / 1e3, # W_fi main beam [cm³]
(0.17 + 0.17 + 0.09 + 1.32 + 0.06 + 0.28 + 1.0 + 0.3 * 2.0) * 4.0 * 8.0**2 / 8, # M_d,fi main [kN m]
118.1e6 / 8664e3, # σ_d,fi main [N/mm²]
(160 - 2 * (30 * 0.8 + 7)) ** 2, # A_fi column [mm²]
(0.17 + 0.17 + 0.09 + 1.32 + 0.06 + 0.28 + 1.0 + 0.3 * 2.0) * 4.0 * 8.0 / 2, # N_d,fi column [kN]
59.0e3 / 9604, # σ_d,fi column [N/mm²]
sqrt(98 * 98**3 / 12 / (98 * 98)), # i_fi column [mm]
3000 / 28.3, # λ_fi column
106.0 / 3.14 * sqrt(21 / (2 / 3 * 11000)), # λ_rel,fi column
1.25 * 21.0 * 0.27, # f_c,0,d,fi column [N/mm²]
# NIST StRD certified values: NumAcc1 and Mavro.
mean(NUMACC1), # mean, NumAcc1
stdev(NUMACC1), # standard deviation, NumAcc1
float(mean(MAVRO)), # mean, Mavro
float(stdev(MAVRO)), # standard deviation, Mavro
]
# Every function the editor offers, in the order of the validation page.
# round() is half away from zero, as in the engine; Python's own round() is
# half to even, so it is computed with Decimal.
half_up = lambda x, places: float(Decimal(x).quantize(Decimal(places), ROUND_HALF_UP))
functions = [
7 if 'exposed' == 'exposed' else 9, 7 if '01' == '1' else 9, 1 if 'exposed' != 'not exposed' else 0, max(30, 1.5 * 25),
7 if 2 >= 2 else 9, 7 if 2 > 2 else 9, 7 if 1 < 2 else None,
sqrt(2), sqrt(16), 27 ** (1 / 3), 16 ** (1 / 4), 2**10, hypot(3, 4),
sin(radians(30)), sin(1), cos(radians(60)), tan(radians(45)), 1 / tan(radians(45)), 1 / cos(radians(60)), 1 / sin(radians(30)),
asin(0.5), acos(0.5), atan(1), asin(0.5), acos(0.5), atan(1), atan2(1, -1),
sinh(1), cosh(1), tanh(1), asinh(1), acosh(2), atanh(0.5),
log(8, 2), log10(1000), log2(32), log(10), exp(1),
abs(-3.5), -1, floor(2.7), ceil(2.1), half_up('2.5', '1'), half_up('3.14159', '0.01'), trunc(-2.7),
max(3, 2500 / 1000), min(3, 7, 5), sum([1, 2, 3, 4]), 2 * 3 * 4, mean([2, 4, 9]), median([3, 1, 4, 1, 5]), stdev([2, 4, 4, 4, 5, 5, 7, 9]),
17 % 5, gcd(12, 18), lcm(4, 6),
]
if __name__ == '__main__':
print(json.dumps({'benchmarks': benchmarks, 'published': published, 'functions': functions}, indent=2))
Release gate and engine versions
This page was built from calculation engine 8 (mathjs 15.2.0), commit cf960d3a5648 on 2026-11-13: 3,368 of 3,368 checks passed.
The checks on this page run before every release of the MathCanvas app and the calculation API, and when this page is built; every worksheet we ship is recalculated and compared with its recorded results. If anything fails, the release stops. Every change that can alter a result gets a new engine version, and every confirmed calculation error becomes a permanent check. The report of each version is archived.
| Engine | Date | Change |
|---|---|---|
| 1 | Before 2026-10-30 | First public calculation engine. |
| 2 | 2026-10-30 | Formulas are read into one explicit tree; notation with two readings is refused with a reason; results carry their working. |
| 3 | 2026-10-30 | Exact psi, ksi, horsepower, acre and torr (mathjs rounds them, the largest error 9 × 10⁻⁷ for acre); min after a number is the minute; displays round the decimal value (2.675 shows as 2.68, not 2.67); temperature units take no prefix (1.2e-5 1/K, not 12 MK⁻¹); a result is displayed in its own units, whatever was calculated before (after 1 sqft, 2.5 m² showed as 26.91 sqft). |
| 4 | 2026-10-31 | Division is a drawn fraction only: a formula with a slash (q·L²/8, 12 kN/m, 5 kN/2 m) gets no answer and the reason "Division needs a fraction". The editor never writes a slash: typing / draws a fraction, and the unit list writes kN/m as one. Version 3 read an unambiguous slash such as q·L²/8 and refused only a slash followed by a product. |
| 5 | 2026-10-31 | A fraction is multiplied only with a visible dot. A fraction touching a factor (⅛q·L², x½, ½(a+b)) gets no answer and the reason "Put · next to a fraction"; the editor writes the dot itself (⅛·q·L², 2·½), and a number before a fraction of units stays a quantity (12 kN/m). Version 4 computed ⅛q·L² as drawn, ⅛·q·L². |
| 6 | 2026-11-02 | Conditional checks: if(condition, when true, when false), comparisons including ≥, ≤, ≠ and =, and quoted text results. Only the selected branch is evaluated. Text results remain upright and quoted, including numeric-looking text. |
| 7 | 2026-11-02 | Structured program blocks with local assignments, if / else if / else, nested branches and one return expression, lowered to the same pure calculation engine. Text equality and inequality compare exact strings, including numeric-looking strings. Programs publish only their named result. |
| 8 | 2026-11-03 | A prime is part of a name, as in Mathcad: Bar′, A′_bar and d′_s are their own variables in every form the editor writes (A_bar′ is A′_bar). Version 7 read a prime as a transpose, so Bar′ gave "Bar is not defined", or silently the value of Bar when Bar existed. A prime after a number or a bracket is refused. Combo boxes: a table of labelled rows with a unit row; with several value columns the selected row is read by index, Bar′_1, Bar′_2, as Mathcad's Bar′[1, Bar′[2. |
Method and independent review
A written verification plan states what we claim, how each claim is evidenced, the acceptance criteria and how changes are controlled. A reviewer pack collects the plan, the release report of one frozen engine version, every case with its source, the discrepancies we found in sources and the test code. Our quality statement describes how we version, test and handle reported errors.
No independent review has taken place yet. If you are a reviewer, a university group or a firm assessing MathCanvas, contact us for the reviewer pack.
Where we are
The road to independent review
No software is trusted on its own word. We work through these steps in order, and an independent reviewer has the last word.
- Done
Read every formula correctly
One meaning or no answer. Thousands of checks run before every release.
- Done
Never break what works
Every worksheet we ship is recalculated on every release, each release’s report is archived, and PDFs can print the working.
- Done
More proof from outside
Published answers from four official sources, every unit and function checked, and the tests themselves tested with planted mistakes.
- We are here
Ready for an independent reviewer
The reviewer pack and our quality statement are written. Next, an engineer outside the project tries the review.
- Next
Independent review
An independent engineer or university reviews one engine version. We publish their findings and our answers.
Found a number that looks wrong?
Send us the formula, the inputs and the value you expected. A confirmed error is fixed and added to these checks for good. Reviewers can ask for the reviewer pack here too.