Kinetic energy calculator
Choose what to solve for, fill in the other two quantities and read the answer. The box for the quantity you solve for is ignored. Energy is shown in joules or kilojoules, and the momentum of the moving body is listed too.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Pick the quantity to solve for: kinetic energy, mass or speed.
- Fill in the other two quantities and choose their units. The box of the quantity you solve for is ignored.
- Read the result in the big figure. The list also shows the other values and the momentum.
How it works
The formula is E = ½mv². Rearranged, m = 2E ÷ v² and v = √(2E ÷ m). Inputs are converted to kilograms, metres per second and joules (1 lb = 0.45359237 kg, 1 mph = 0.44704 m/s, 1 km/h = 1/3.6 m/s), calculated, and converted back for display.
Worked example
A 2 kg ball moving at 3 m/s has E = ½ × 2 × 3² = 9 J. A 1,000 kg car at 36 km/h (10 m/s) has E = ½ × 1000 × 10² = 50,000 J, which is 50 kJ.
Tips
- Use the same body for mass and speed; energy depends on both.
- Results are shown with six significant digits, so do not read more precision into them than your inputs have.
Frequently asked questions
What is the kinetic energy formula?
Kinetic energy is E = ½ × m × v², where m is the mass in kilograms and v the speed in metres per second, giving joules. The calculator converts grams, pounds, km/h and mph to these units first.
Why does doubling the speed quadruple the energy?
Speed is squared in the formula. At twice the speed the energy is 2² = 4 times larger, and at three times the speed it is 9 times larger. Doubling the mass only doubles the energy.
Is this the energy of a car crash?
It is the kinetic energy of the moving body, which is a starting point. Real crashes also depend on how the energy is absorbed, how long the stop takes and the structure involved, which this tool does not model.
What does the solved mass or speed assume?
It assumes a single non-rotating body moving at speeds far below the speed of light, which is the school-physics case. Rotation adds a separate energy term that is not included.