Size a rain tank from a monthly mass balance: catchment area times rainfall times runoff coefficient against household demand, month by month. The worst cumulative shortfall sets the volume, and that volume over the daily demand gives the days of autonomy.
| Month | Rain (mm) | Harvest (L) | Demand (L) | Net (L) | Stored (L) | Cumulative shortfall (L) |
|---|
Henderson-Hasselbalch against the useful pKa +- 1 band, and the exact charge-balance pH for a real recipe.
Euler-Bernoulli tip deflection and bending stress for a rectangular section, with a factor of safety.
Layer-by-layer wall transmittance, the linear thermal bridge value and whether the internal surface will condense.
Reflected light off a coated surface: reflectance and hue from film thickness, refractive index and incidence angle, with a plot across the visible band.
Estimate doubling time and project compound growth, with the exact doubling time beside the estimate so you can see where the rule drifts.
Tax owed, effective rate and marginal rate from gross income and deductions, using a fixed published bracket table so the arithmetic is reproducible.
Discount a lump sum, ordinary annuity or annuity due back to today, and see the interest the discount rate is actually charging you.
Break-even volume and revenue from fixed and variable costs, plus profit and margin at a target volume. Handles the case where there is no break-even at all.
