About this calculator
Choose kinetic energy (energy of movement) or potential energy (energy stored by height), enter the mass and the speed or height, and get the energy in joules, with the working.
For potential energy you can choose the gravity of Earth, the Moon, Mars or Jupiter.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
2 kg moving at 10 m/s
- Kinetic energy
- 100 J
- In kilojoules
- 0.1 kJ
- In watt-hours
- 0.027778 Wh
- Momentum
- 20 kg·m/s
2 kg moving at 10 m/s has 100 J of kinetic energy.
Show the working
- Kinetic energy = ½ × mass × speed².
- = ½ × 2 × 10² = ½ × 2 × 100 = 100 J.
- Doubling the speed quadruples the energy, because speed is squared.
A 1,000 kg car at 30 m/s (about 67 mph)
- Kinetic energy
- 450,000 J
- In kilojoules
- 450 kJ
- In watt-hours
- 125 Wh
- Momentum
- 30,000 kg·m/s
1,000 kg moving at 30 m/s has 450,000 J of kinetic energy.
Show the working
- Kinetic energy = ½ × mass × speed².
- = ½ × 1,000 × 30² = ½ × 1,000 × 900 = 450,000 J.
- Doubling the speed quadruples the energy, because speed is squared.
2 kg raised 10 m on Earth
- Potential energy
- 196.133 J
- In kilojoules
- 0.196133 kJ
- In watt-hours
- 0.054481 Wh
2 kg raised 10 m on Earth stores 196.133 J of gravitational potential energy.
Show the working
- Potential energy = mass × gravity × height.
- = 2 × 9.80665 × 10 = 196.133 J.
The formulas
- Kinetic energy: KE = ½ × m × v², where m is mass in kg and v is speed in m/s.
- Gravitational potential energy: PE = m × g × h, where g is gravity (9.80665 m/s² on Earth) and h is height in metres.
Both give energy in joules (J).
Why speed matters so much
Kinetic energy depends on the square of speed. Doubling your speed quadruples the energy, which is why a crash at 60 mph is far more than twice as violent as one at 30 mph, and why stopping distances grow so quickly.
Energy changes form
Energy is never lost, only changed. A ball dropped from height loses potential energy and gains the same amount of kinetic energy (ignoring air resistance). Use the energy converter to express the answer in kilowatt-hours or calories.
Frequently asked questions
What is the formula for kinetic energy?
KE = ½ × mass × speed².
What is the formula for potential energy?
PE = mass × gravity × height.
What units does it use?
Kilograms, metres per second and metres, giving joules.
Why is gravity different on the Moon?
The Moon has less mass, so its surface gravity is about 1.62 m/s², roughly a sixth of Earth's.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.