Force, Work & Power
F = ma, W = Fd cos θ and P = W/t or Fv, each solved for any variable, in kg/lb, m/s²/g, N/kN/lbf/kgf, m/ft/mi, s/min/h and km/h/mph — SI and imperial.
The force, mass, acceleration, work, distance, power, time or speed you left blank, plus the force in N, kN, lbf and kgf, work in J, ft·lbf, kWh and cal, and power in W, kW, hp and ft·lbf/s.
Example: 1 200 kg × 2.5 m/s² is 3 000 N (674 lbf, 306 kgf); 50 N over 10 m at 30° does 433 J; 3 000 J in 4 s is 750 W (1.01 hp); pushing with 400 N at 90 km/h takes 10 kW.
Newton's second law
and what it costs to move.
The three relations, the angle in the work formula, and where the unit factors come from.
Force
F = m·a: the net force on a body equals its mass times its acceleration. Mass is converted to kilograms and acceleration to m/s² (g = 9.80665 m/s², 1 ft/s² = 0.3048 m/s²), so the result is in newtons and then also shown in kN, pounds-force (1 lbf = 4.448 221 6 N) and kilograms-force (1 kgf = 9.80665 N). "Net" matters: if several forces act, a is set by their vector sum, and a body at rest on a table has zero net force.
Work
W = F·d·cos θ — only the part of the force along the motion does work. At 0° the whole force counts, at 90° none of it (carrying a bag horizontally does no work on it, however tiring), and beyond 90° the work is negative because the force opposes the motion, as friction does. One joule is one newton-metre; the table also gives ft·lbf, kWh and calories. Solving for F or d divides by cos θ, so at exactly 90° there is no solution and the page says so.
Power
Power is work per time, P = W ÷ t, or force times speed for a steady push, P = F·v·cos θ — the same thing, since d ÷ t = v. One watt is one joule per second; mechanical horsepower is 745.6999 W (the metric PS is 735.5 W). Conversion factors follow NIST SP 811. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- F = m·a; W = F·d·cos θ; P = W ÷ t = F·v·cos θ; g = 9.80665 m/s², 1 lbf = 4.4482216 N, 1 kgf = 9.80665 N, 1 hp = 745.6999 W, 1 ft·lbf = 1.3558179 J (NIST SP 811 factors)
Last reviewed 22 September 2026. How results are checked: How we verify.