Four core mechanics formulas in one free calculator: kinetic energy (½mv²), gravitational potential energy (mgh), work done by a force (W = Fd cos θ) and power (P = W/t). Leave one box empty and it solves for that value, in J, kJ, kWh, W or horsepower.
Energy, work and power formulas
Worked examples
- A 1,200 kg car at 100 km/h (27.8 m/s) has KE = ½ × 1200 × 27.8² ≈ 463 kJ. Doubling speed quadruples kinetic energy, which is why braking distance rises so fast.
- Lifting 50 kg by 10 m stores PE = 50 × 9.81 × 10 = 4,905 J. Doing it in 5 s needs 981 W, about 1.3 hp.
- Pulling a sledge 15 m with 200 N at 30° above horizontal does W = 200 × 15 × cos 30° = 2,598 J of work.
Frequently asked questions
How do you calculate kinetic energy?
KE = ½mv², with mass in kg and speed in m/s, giving joules. Enter mass and speed (km/h is converted for you) and leave energy empty.
How do you calculate potential energy?
Gravitational PE = mgh: mass × gravitational field strength × height. A 2 kg book on a 1.5 m shelf has about 29.4 J.
What is the difference between work and power?
Work is energy transferred by a force (joules). Power is how fast that work is done (watts = joules per second).
Why does the angle matter for work?
Only the part of the force along the motion does work: W = Fd cos θ. Pushing at 90° to the motion does no work.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.