Kinetic Energy Calculator (KE = ½mv²)
Find the kinetic energy of a moving object, or rearrange to solve for mass or speed.
SI units: joules (kg·m²/s²), kilograms, m/s.
Double the speed and kinetic energy quadruples — the curve is a parabola in v.
Kinetic energy is the energy of motion: KE = ½ × m × v², with mass in kilograms and speed in metres per second, giving an answer in joules. A 2 kg object moving at 3 m/s has KE = ½ × 2 × 3² = ½ × 2 × 9 = 9 J. Because v is squared, doubling the speed quadruples the energy.
What is kinetic energy?
Kinetic energy is the work an object can do because it is moving — the energy you must add to bring a resting mass up to speed, and the energy released when it is brought back to rest. It depends on two things: how much mass is moving and how fast. The mass enters linearly, but the speed enters as a square, so speed dominates: a small, fast object can carry far more energy than a large, slow one.
KE = kinetic energy (J), m = mass (kg), v = speed (m/s)
Worked example
A 2 kg object travels at 3 m/s. How much kinetic energy does it carry?
- 1 Write the formula. KE = ½ × m × v², with mass in kilograms and speed in m/s.
- 2 Square the speed. v² = 3 m/s × 3 m/s = 9 m²/s².
- 3 Multiply by mass and one half. KE = ½ × 2 kg × 9 = 9 J — the answer is in joules.
How kinetic energy scales with mass and speed
With v squared, doubling the speed quadruples the energy; doubling the mass only doubles it.
| Mass (kg) | Speed (m/s) | KE = ½mv² (J) |
|---|---|---|
| 2 | 1 | 1 |
| 2 | 2 | 4 |
| 2 | 3 | 9 |
| 2 | 6 | 36 |
| 4 | 3 | 18 |
| 1 | 10 | 50 |
Units, the v² rule, and energy conservation
The joule is the SI unit of energy. One joule equals 1 kg·m²/s², so as long as you put mass in kilograms and speed in metres per second, KE comes out in joules with no conversion. Mixing in grams or km/h is the most common source of wrong answers.
Speed matters far more than mass. Because the speed is squared, going from 3 m/s to 6 m/s raises the energy by a factor of four, not two. This is why stopping distance and impact damage rise so steeply with speed.
Kinetic vs potential energy. Kinetic energy is energy of motion; gravitational potential energy (PE = mgh) is stored energy of position. As an object falls, PE converts into KE while the total stays constant, which is the principle behind conservation of mechanical energy.