Elastic and inelastic collision calculator
Enter each mass and its velocity before impact; a negative velocity means moving the opposite way.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter collision type, mass of body 1, velocity of body 1, mass of body 2 and velocity of body 2.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Elastic: v₁′ = ((m₁ − m₂)v₁ + 2m₂v₂) ÷ (m₁ + m₂), v₂′ = ((m₂ − m₁)v₂ + 2m₁v₁) ÷ (m₁ + m₂). Perfectly inelastic: v′ = (m₁v₁ + m₂v₂) ÷ (m₁ + m₂).
Example
Inputs: Collision type = Perfectly elastic, Mass of body 1 = 2 kg, Velocity of body 1 = 3 m/s, Mass of body 2 = 1 kg, Velocity of body 2 = 0 m/s. Result: Body 1 velocity after: 1 m/s; Body 2 velocity after: 4 m/s; Total momentum (conserved): 6 kg·m/s.
Limits and caveats
- Covers the two limiting cases only; real collisions fall somewhere between them.
- Assumes a head-on collision along one line with no outside forces.
Questions about this tool
What is the difference between elastic and inelastic collisions?
In an elastic collision both momentum and kinetic energy are conserved; in a perfectly inelastic one the bodies stick and only momentum is conserved.
Where does the lost energy go?
It turns into heat, sound and deformation, while total energy is still conserved.
What happens when two equal balls collide elastically?
They swap velocities: the moving ball stops and the resting one moves off at its speed, as with billiard balls.