Kinetic Energy Calculator with Potential Energy, Work and Power
How the kinetic energy calculator works: KE = ½ · m · v². A 1,000 kg car at 50 km/h (13.9 m/s, 31 mph) carries about 96 kJ – the same as falling from 9.8 m. Because velocity is squared, doubling the speed quadruples the energy.
Example: What do you want to calculate: Kinetic energy (mass, velocity) · Mass m 1,000 kg · Velocity v 50 · Unit: km/h → Result: KE = 96,450 J (96.45 kJ). Source: OpenStax, OpenStax University Physics Vol. 1, 7.2 Kinetic Energy and 8.1 Potential Energy of a System. Updated: .
How it is calculated
Kinetic energy formula
The kinetic energy of a body with mass m moving at velocity v is
KE = ½ · m · v² · rearranged: v = √(2 · KE / m)
Units: mass in kg, velocity in m/s, energy in joules (1 J = 1 kg·m²/s²). Convert km/h by dividing by 3.6 and mph by multiplying by 0.44704.
Worked example
- Car: m = 1,000 kg, v = 50 km/h = 13.89 m/s
- KE = ½ · 1,000 kg · (13.89 m/s)² = 96,451 J ≈ 96.5 kJ
- At 100 km/h: 385.8 kJ – four times as much. That is why braking distance grows with the square of speed.
The other basic formulas
| Quantity | Formula | Unit |
|---|---|---|
| Potential energy | PE = m · g · h | J |
| Work | W = F · d · cos θ | J = N·m |
| Power | P = W / t | W = J/s |
| Force (Newton’s second law) | F = m · a | N = kg·m/s² |
g is standard gravity, 9.806 65 m/s² (NIST/CODATA). For work only the force component along the motion counts: at 60° it is half, at 90° no work is done.
Conservation of energy
Without friction, potential energy turns completely into kinetic energy: m · g · h = ½ · m · v², so v = √(2 · g · h) and mass cancels out. That is why the calculator shows the equivalent drop height for every kinetic energy. Conversions: 1 Wh = 3,600 J, 1 kcal = 4,184 J, 1 ft·lbf = 1.3558 J (NIST SP 811).
Frequently asked questions
How do you calculate kinetic energy?
KE = ½ · m · v² with mass in kg and velocity in m/s. Example: 80 kg at 5 m/s = ½ · 80 · 25 = 1,000 J.
How do you find velocity from kinetic energy?
Rearrange: v = √(2 · KE / m). 1,000 J and 80 kg give √(2,000 / 80) = 5 m/s.
How do you convert kinetic energy from joules to ft-lbs?
Divide joules by 1.3558. For example, 3,000 J ≈ 2,213 ft·lbf – the unit often used for bullets and arrows in the US.
How do you calculate work done in physics?
Work = force × distance along the force: W = F · d · cos θ. Pushing a box with 100 N over 10 m takes 1,000 J.
What is the difference between work and power?
Power is work per unit time: P = W / t. 1,000 J in 10 s is 100 W; the same work in 2 s is 500 W.
Sources and legal basis
- OpenStax: OpenStax University Physics Vol. 1, 7.2 Kinetic Energy and 8.1 Potential Energy of a System
- CODATA: NIST CODATA – standard acceleration of gravity g_n = 9.806 65 m/s² (exact)
- NIST SP 811 App. B.9: NIST SP 811 – Guide for the Use of the SI, Appendix B.9: calorie (thermochemical) = 4.184 J, watt hour = 3600 J
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