Math & Numbers

Convert dilution notations 1:X ↔ 1/X ↔ percent, with dilution factor, parts, and mixing volumes.

Math & Numbers

Convert dynamic (absolute) viscosity between Pa·s (pascal-second, SI base, = N·s/m² = kg/(m·s)), cP (centipoise, 1 cP = 0.001 Pa·s), and lbf·s/ft² (imperial, 1 = 47.88025898 Pa·s). Converts via Pa·s to the target unit and also lists the equivalent value in all three units for reference. Reference values: water 20°C ≈ 1.002 cP, glycerol 20°C ≈ 1412 cP, air 20°C ≈ 0.0181 cP.

Math & Numbers

Compute the air dew-point temperature from dry-bulb temperature and a humidity reading using the Magnus saturation-pressure equation: P_ws(T) = 0.6108·exp(17.27·T/(T+237.3)), P_w = φ·P_ws, T_dp = 237.3·ln(P_w/0.6108) / (17.27 − ln(P_w/0.6108)). Also returns the saturation vapour pressure P_ws, actual partial pressure P_w, and absolute humidity ρ_v (kg/m³). Three input modes: relative humidity φ (natural ventilated), August natural-ventilated wet-bulb T_w, or aspirated (Assmann) wet-bulb T_wa. Temperature in °C/K/°F; all reported temperatures are in the selected Temperature Unit.

Math & Numbers

Compute the drag force on a body in a fluid stream: F_D = ½·ρ·v²·C_D·A (N), where ρ is the fluid density, v the free-stream velocity, C_D the drag coefficient (shape- and Reynolds-dependent), and A the reference (frontal projected) area. A built-in shape library supplies typical high-Re C_D values: sphere 0.47, hemisphere 0.42, long cylinder 0.81, disk/flat plate 1.17, cube 1.05, streamlined airfoil 0.04, long streamlined ellipsoid 0.07, cone 0.50; or choose 'Custom' to enter C_D directly. Optionally, with dynamic viscosity μ and characteristic length L, the Reynolds number Re = ρ·v·L/μ is computed, and the power dissipated by drag P = F_D·v (W). Density in kg/m³/g/cm³, velocity in m/s/km/h, area in m²/cm²/mm², length in m/cm/mm.

Math & Numbers

Size a duct cross-section from the air flow rate Q and the design mean velocity v: area A = Q/v. Circular duct diameter D = √(4A/π). Rectangular duct with aspect ratio r = a/b gives b = √(A/r) and a = r·b, plus the ASHRAE equivalent diameter D_eq = 1.30·(a·b)^0.625/(a+b)^0.25. Flow rate in m³/s/m³/h/CFM, velocity in m/s; dimensions reported in mm and inches.

Math & Numbers

Convert between the three common refrigeration efficiency metrics: COP (dimensionless, W/W), EER (Btu/(W·h)), and SEER (seasonal Btu/(W·h)). Standard relations: COP = EER / 3.412, EER = COP × 3.412, SEER = EER / α (α seasonal weighting factor, default 0.875, adjustable 0.8–0.91 to match regional standards such as ARI 210/240). Enter any one metric and all three are reported.

Math & Numbers

Compute radial steady-state heat conduction through a single-layer cylindrical wall (Fourier's law in cylindrical coordinates): radial heat flow rate Q = 2π·k·L·ΔT/ln(r₂/r₁) (W), inner-surface heat flux q_inner = Q/(2π·r₁·L) (W/m²), outer-surface heat flux q_outer = Q/(2π·r₂·L) (W/m²), and cylindrical thermal resistance R = ln(r₂/r₁)/(2π·k·L) (K/W). k is the thermal conductivity (W/(m·K)); L the cylinder length; r₁ the inner radius, r₂ the outer radius (must have r₂ > r₁ > 0); ΔT the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9). ΔT may be negative (indicating reverse heat flow), but k, L, r₁ and r₂ must be positive. Length and radius in m/cm/mm.

Math & Numbers

Compute the back-EMF and electromagnetic torque of a DC motor from its machine constant: E=k·ω, T=k·I. In SI units the back-EMF constant equals the torque constant (k_e=k_t=k, V·s/rad=N·m/A). Also returns the mechanical (air-gap) power P=T·ω=E·I. Speed accepted in rad/s or RPM.

Math & Numbers

Look up and compute the maximum deflection for four classic beam cases: cantilever with end point load (δ=PL³/3EI), cantilever with UDL (δ=qL⁴/8EI), simply supported with mid-span point load (δ=PL³/48EI), and simply supported with UDL (δ=5qL⁴/384EI).

Math & Numbers

Step-by-step factor-label unit cancellation with inverted-factor diagnosis and optional student-answer checking.

Finance

Convert an amount between currencies using live exchange rates from a free, no-key API (open.er-api.com). Supports 160+ world currencies. Shows the converted amount, the exchange rate used, a comparison table against popular currencies, and the rate update timestamp.

Finance

General-purpose debt payoff planner comparing avalanche, snowball, and minimum-only strategies. Enter debts as 'name, balance, APR%, minPayment $' per line plus an extra monthly payment. Shows payoff time, total interest, savings, balance decline curves, and a per-debt repayment detail table.