Kinetic & Potential Energy
KE = ½mv², gravitational PE = mgh and elastic PE = ½kx², solved for any variable, in kg/lb, m/s, km/h, mph, m/ft, with your g and J, kJ, cal, Wh, ft·lbf out.
The energy, mass, speed, height, spring constant or extension you solved for, the energy in every unit, and the same energy as the other form — the height a moving body could climb or the landing speed.
Example: A 1 500 kg car at 100 km/h carries 578.7 kJ — enough to climb 39.3 m; 70 kg at 10 m stores 6.86 kJ and would land at 14.0 m/s; a 200 N/m spring stretched 5 cm holds 0.25 J.
Half m v squared,
m g h, half k x squared.
The three formulas, how each unknown is isolated, and what the other-form equivalent means.
The formulas
Kinetic energy is ½·m·v² — it grows with the square of the speed, so doubling the speed quadruples the energy. Gravitational potential energy is m·g·h, measured from whatever level you take as zero, with g = 9.80665 m/s² (standard gravity) unless you change it — 1.62 for the Moon, 3.71 for Mars. Elastic potential energy in a spring obeying Hooke's law is ½·k·x² with k in N/m and x the stretch or compression from the natural length. Each formula is rearranged for the variable you choose: m = 2E ÷ v², v = √(2E ÷ m), h = E ÷ mg, and so on.
Units
Inputs are converted to SI first — kg (1 lb = 0.45359237 kg), m/s (1 km/h = 1 ÷ 3.6 m/s, 1 mph = 0.44704 m/s), m — and the result is converted back to the unit you asked for. Energy is reported in joules and, in the table, in kJ, calories (4.184 J), kilocalories, watt-hours (3 600 J), foot-pound-force (1.3558 J) and electron-volts (1.602 176 634 × 10⁻¹⁹ J, an exact SI value).
The equivalent
Energy is conserved without friction or drag, so a body's kinetic energy tells you how high it could rise (h = v² ÷ 2g) and a body's potential energy tells you how fast it would be moving after falling that far (v = √(2gh)). The page shows that conversion as a note; real objects lose energy to air resistance, so the true height is lower and the true landing speed slower. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- KE = ½·m·v²; PE = m·g·h with g = 9.80665 m/s² unless changed; elastic PE = ½·k·x²; 1 cal = 4.184 J, 1 Wh = 3 600 J, 1 ft·lbf = 1.35582 J, 1 lb = 0.45359237 kg (SI / NIST factors)
Last reviewed 22 September 2026. How results are checked: How we verify.