Engineering & finance
Calculators
Four transparent calculators with formulas and unit-aware results.
Units are shown on each field, and each calculator lists its valid inputs. These are study and checking aids, not tools for operational or safety decisions.
Darcy–Weisbach pressure loss
All inputs must be greater than zero; roughness can be zero. Assumes a full circular pipe and constant fluid density.
ΔP = f(L/D)(ρv²/2). Laminar: f = 64/Re. Turbulent (Swamee–Jain): f = 0.25/[log₁₀(ε/(3.7D) + 5.74/Re⁰·⁹)]².
Hydrostatic pressure
Depth and density must be greater than zero. Assumes one constant density over the full depth.
P = ρgh, with g = 9.80665 m/s². Gauge pressure excludes atmospheric pressure.
Ideal gas volume at new conditions
Volume and absolute pressures must be greater than zero; temperatures must be above −273.15 °C.
P₁V₁/T₁ = P₂V₂/T₂ → V₂ = V₁(P₁/P₂)(T₂/T₁). Temperatures use kelvin; pressures must be absolute.
NPV and simple payback
Investment must be positive and annual cash flow non-zero (it can be negative). Use whole years and a discount rate above −100%. Assumes the same cash flow every year.
NPV = −I + Σₜ₌₁ⁿ CF/(1+r)ᵗ. Simple payback = I/CF; payback ignores discounting and cash flows after recovery.