Kinetic energy is the energy of motion, potential energy the energy of height. A 1,500 kg car at 50 km/h carries ½ × 1,500 × 13.89² = 144,676 J, about 145 kJ – as much as it would gain falling from 9.8 m. Choose kinetic or potential, type the mass and the speed or height in any units, and the calculator converts to SI, works out the energy step by step and shows it in joules, watt-hours and kilocalories.
A family car (1,500 kg) at different speeds
| Speed | Kinetic energy | Same as a fall from |
|---|---|---|
| 30 km/h (19 mph) | 52 kJ | 3.5 m |
| 50 km/h (31 mph) | 145 kJ | 9.8 m |
| 80 km/h (50 mph) | 370 kJ | 25.2 m |
| 100 km/h (62 mph) | 579 kJ | 39.3 m |
| 130 km/h (81 mph) | 978 kJ | 66.5 m |
At 50 km/h a crash releases the energy of a fall from about three stories up; at 100 km/h, from about thirteen. That is one reason speed limits are low near schools: the energy, and the braking distance, grow with the square of the speed.
The two formulas
| Energy | Formula | Units |
|---|---|---|
| Kinetic | KE = ½ m v² | kg, m/s → J |
| Gravitational potential | PE = m g h | kg, m/s², m → J |
| Fall speed (PE turned into KE) | v = √(2 g h) | m/s |
The potential energy is counted from a level you choose, such as the floor or the ground; only the difference in height matters.
Joules in everyday terms
| Energy | About |
|---|---|
| 1 J | lifting an apple (100 g) by 1 m |
| 4,184 J (1 kcal) | the energy in a food Calorie |
| 145 kJ | the car at 50 km/h above, or 35 kcal |
| 3.6 MJ (1 kWh) | a 2 kW kettle running for 30 minutes |
Exam tip: convert km/h to m/s (divide by 3.6) and grams to kilograms before you square anything. The calculator shows these conversions as its first steps, and it works offline for homework anywhere.
Frequently asked questions
What is the formula for kinetic energy?
KE = ½ × m × v², with the mass in kilograms and the speed in meters per second; the answer is in joules. A 1,500 kg car at 50 km/h (13.89 m/s) has 0.5 × 1,500 × 13.89² = 144,676 J, about 145 kJ.
What is the formula for potential energy?
PE = m × g × h. Lifting 10 kg by 2 m on Earth stores 10 × 9.80665 × 2 = 196 J.
Why does doubling the speed quadruple the energy?
Because speed is squared in the formula. At 100 km/h a car carries four times the energy it has at 50 km/h, and needs about four times the distance to brake to a stop.
How are kinetic and potential energy linked?
When something falls, potential energy turns into kinetic energy: m g h = ½ m v², so v = √(2 g h), whatever the mass. A drop from 10 m ends at 14 m/s, if air resistance is negligible.
How many joules are in a kilocalorie or a kilowatt-hour?
1 kcal (the food Calorie) is 4,184 J; 1 Wh is 3,600 J and 1 kWh is 3.6 million J.
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