Math & Numbers

Bézout coefficients for any-sign integers with the full division-step table, lcm, and optional linear Diophantine solving (particular + general solution).

Math & Numbers

Explicit Euler integration for dy/dx = f(x, y): step table, final estimate, and optional exact-solution error column.

Math & Numbers

Solve separable dy/dx = g(x)·h(y) symbolically: H(y) = G(x) + C, explicit inversion, initial conditions, and partial fractions for quadratics like y(1−y).

Math & Numbers

Convert force between newton (N, SI base), kilonewton (kN), dyne (dyn, CGS = 10⁻⁵ N), pound-force (lbf = 4.4482216152605 N), kilogram-force (kgf = 9.80665 N), and poundal (pdl = 0.138254954376 N). All factors derive from the exact defining constants 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, and standard gravity g₀ = 9.80665 m/s². Converts via newton to the target unit and lists the equivalent value in all six units. Reference: 1 kg of mass on Earth ≈ 9.80665 N (1 kgf); an adult weighs ≈ 700 N.

Math & Numbers

Convert fuel consumption / fuel economy between L/100km, miles per US gallon (mpg US), miles per Imperial gallon (mpg UK), and km/L. mpg and L/100km are reciprocal (higher mpg = lower L/100km), so conversion goes through the km/L axis, not a single multiplier. Defining constants are exact by law: 1 US gallon = 3.785411784 L (NIST HB 44), 1 Imperial gallon = 4.54609 L (UK W&M Act 1985), 1 mile = 1.609344 km (1959 agreement). Reference: a compact car at ~6 L/100km ≈ 39 mpg US ≈ 47 mpg UK.

Math & Numbers

Convert mass flow rate between kg/s (kilograms per second, SI base), lb/h (pounds per hour, 1 lb = 0.45359237 kg), and t/h (tonnes per hour, 1 t = 1000 kg). Converts via kg/s to the target unit and also lists the equivalent value in all three units for reference. Used for boiler feedwater, chemical dosing, fuel consumption, and compressed-gas metering.

Math & Numbers

Convert volumetric flow rate between m³/h (cubic metres per hour), L/min (litres per minute), gpm (US gallons per minute, 1 gal = 3.785411784 L), and cfm (cubic feet per minute, 1 ft³ = 28.3168466 L). Converts via m³/s to the target unit and also lists the equivalent value in all four units for reference. Used for pumps, HVAC, compressed air, and piping.

Math & Numbers

Mean-stress fatigue correction under cyclic loading. Given stress amplitude σ_a, mean stress σ_m, and material σ_uts / σ_-1 (endurance limit) / σ_y, compute safety factors from three classical criteria: Modified Goodman (linear, conservative), Gerber (parabolic, better for ductile metals), and Soderberg (uses σ_y, most conservative). Reports the governing (smallest) value and whether the operating point lies inside the Goodman line.

Math & Numbers

Estimate multi-segment trip fuel, cost, CO2, route-condition weighting, and carpool sharing.

Math & Numbers

Calculate the gear module m. m = d/z = p/π. Solve the module from the pitch diameter d and tooth count z, or from the circular pitch p. Also returns the pitch diameter, circular pitch and addendum.

Math & Numbers

Calculate the kinetic energy stored in a flywheel. E = ½·I·ω², ω = 2π·n/60. Enter the moment of inertia directly, or compute it from flywheel mass and radius (I = ½·m·r²). Supports J/kJ/Wh.

Math & Numbers

Calculate the gear ratio and output speed of a meshing gear pair. i = z₂/z₁ = n₁/n₂. Enter the tooth counts to get the ratio; add the driver speed to get the driven speed.