The numbers, checked.
Each case below states a claim, the source it comes from, and an independent re-implementation of the relationship. Nothing on this page calls the calculator code — if the two disagree, the case fails.
Finance
14 / 14 passingScroll for expected / computed →
| Calculator | Reference | Expected | Computed | Δ | Status |
|---|---|---|---|---|---|
| Mortgage Payment $336,000 at 6.40% over 30 years | Annuity-immediate: P·r/(1−(1+r)⁻ⁿ), r = APR/1200 | 2,101.70$/mo | 2,101.70$/mo | 0.000% | Pass |
| Auto Loan $27,630 financed at 7.20% over 60 months | Level-payment amortisation, monthly compounding | 549.72$/mo | 549.72$/mo | 0.000% | Pass |
| Student Loan $38,000 at 6.10% over 10 years | 34 CFR 685.208 standard repayment mechanics | 423.79$/mo | 423.79$/mo | 0.000% | Pass |
| Compound Interest $10,000 at 7% compounded monthly for 10 years | FV = P(1 + r/n)^(nt) | 20,096.61$ | 20,096.61$ | 0.000% | Pass |
| APY 6% nominal compounded monthly | Regulation DD: APY = (1 + r/n)^n − 1 | 6.1678% | 6.1678% | 0.000% | Pass |
| CAGR $10,000 → $25,000 over 10 years | CAGR = (Vₙ/V₀)^(1/n) − 1 | 9.5958% | 9.5958% | 0.000% | Pass |
| Bond Duration 5% coupon, 10-year, $1,000 face at a 5% yield | Discounted cash flows; a par bond prices at face | 1,000.00$ | 1,000.00$ | 0.000% | Pass |
| Black–Scholes S = K = 100, r = 4%, σ = 20%, T = 1 | Black–Scholes (1973) closed form | 9.9250$ | 9.9250$ | 0.000% | Pass |
| Kelly Criterion p = 0.55, net odds b = 1.2 | Kelly (1956): f* = (p(b+1) − 1)/b | 17.50% | 17.50% | 0.000% | Pass |
| NPV −$100k then 30/35/40/45/50k at 10% | NPV = −C₀ + Σ CFₜ/(1+r)ᵗ | 48,032.61$ | 48,032.61$ | 0.000% | Pass |
| IRR Same cash flows as the NPV case | Root of NPV(r) = 0, bisection to 1e-9 | 25.75% | 25.75% | +0.006% | Pass |
| Break-Even Fixed $240k, price $45, variable $18 | Q* = F/(P − V) | 8,888.89units | 8,888.89units | 0.000% | Pass |
| WACC 60/40 equity/debt, Ke 10.25%, Kd 5.5%, tax 21% | WACC = (E/V)Ke + (D/V)Kd(1−T) | 7.888% | 7.888% | 0.000% | Pass |
| Cap Rate NOI $29,400 on a $420,000 price | R₀ = NOI / price | 7.00% | 7.00% | 0.000% | Pass |
Engineering
9 / 9 passingScroll for expected / computed →
| Calculator | Reference | Expected | Computed | Δ | Status |
|---|---|---|---|---|---|
| Pipe Friction 18 m³/h, D 50 mm, L 60 m, ε 0.045 mm | Darcy–Weisbach with Colebrook–White friction factor | 8.469m | 8.469m | -0.004% | Pass |
| Heat Exchanger Hot 150→90 °C, cold 25→70 °C, counterflow | LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂) | 72.241K | 72.241K | -0.001% | Pass |
| Column Buckling E 200 GPa, I 8.5×10⁻⁶ m⁴, L 6 m, K = 1 | Euler: Pcr = π²EI/(KL)² | 466.06kN | 466.06kN | +0.001% | Pass |
| Weibull Reliability β = 1.8, η = 12,000 h, t = 8,760 h | R(t) = exp[−(t/η)^β] | 56.693% | 56.693% | 0.000% | Pass |
| Reynolds Number Re = 100,000, ε/D = 0.0005 | Colebrook–White (1939) | 0.02033— | 0.02033— | -0.015% | Pass |
| Three-Phase Power 400 V line, 63 A line, pf 0.88 | S = √3·V_L·I_L | 43.648kVA | 43.648kVA | -0.001% | Pass |
| RC Time Constant R = 10 kΩ, C = 100 nF | f_c = 1/(2πRC) | 159.155Hz | 159.155Hz | 0.000% | Pass |
| Wire Gauge AWG 10 conductor | ASTM B258: d = 0.127·92^((36−n)/39) mm | 5.2612mm² | 5.2612mm² | -0.001% | Pass |
| Ideal Gas Law 101.325 kPa, 1 m³, 20 °C | n = PV/RT, R = 8.314462618 J/(mol·K) | 41.5712mol | 41.5712mol | 0.000% | Pass |
Independent
Every compute is written from the formula, not imported from the calculator. The page cannot pass by agreeing with itself.
Sourced
Expected values come from the cited text, standard or closed-form reference — not from a previous run of the site.
Reproducible
The same cases run in the repository test suite. Open a calculator, enter the claim, and compare.