Calculate the kinetic energy of a moving object from its mass and speed — or rearrange the formula to solve for mass or velocity. Uses KE = ½ m v² with SI units (joules).
Kinetic energy is the energy an object has because it is moving. The faster it goes and the more mass it has, the more kinetic energy it carries. The relationship is KE = ½ m v², where mass is in kilograms and velocity in metres per second, giving energy in joules (J).
Because velocity is squared, speed matters far more than mass: doubling the speed multiplies the kinetic energy by four. This is why stopping distances and collision energies rise so steeply with speed.
For the same mass and speed, use the momentum calculator to compare how momentum and kinetic energy change with speed.
This tool calculates translational kinetic energy in classical mechanics. Mass must be positive; kinetic energy and speed must be non-negative. It does not include rotation or potential energy.
The approximation requires speeds much smaller than the speed of light. A note appears from 0.1c; speeds at or above c are rejected. Near light speed, use relativistic kinetic energy, (γ − 1)mc². Velocity here means the magnitude of velocity (speed), not direction.
For the high-speed formula, see OpenStax: Relativistic Energy.
Kinetic energy is KE = ½ m v²: one half times the mass (kg) times the velocity (m/s) squared. The result is in joules.
Rearrange the formula to v = √(2·KE / m). Set 'Solve for' to Velocity, enter the kinetic energy and mass, and the calculator returns the speed.
The SI unit is the joule (J), equal to kg·m²/s². One joule is roughly the energy of a 100 g apple moving at about 4.5 m/s.
Because the work needed to accelerate an object integrates force over distance, and distance grows with the square of the final speed. Doubling speed therefore quadruples the kinetic energy.