By Zencalcy Editorial TeamLast reviewed About us
In a collision between two bodies, total momentum is conserved. The coefficient of restitution sets how much kinetic energy bounces back: 1 for a perfectly elastic collision, 0 for a perfectly inelastic one. This calculator returns both final velocities.
Final velocities for a two-body collision with restitution.
v₁ = ((m₁ − e·m₂)u₁ + (1 + e)m₂u₂) / (m₁ + m₂) v₂ = ((m₂ − e·m₁)u₂ + (1 + e)m₁u₁) / (m₁ + m₂)
Velocities are signed: use positive for one direction and negative for the opposite. Set e = 1 for elastic and e = 0 for a perfectly inelastic collision.
| Symbol | Meaning |
|---|---|
| m₁, m₂ | Masses of the two bodies, in kilograms. |
| u₁, u₂ | Initial velocities, in metres per second (signed). |
| e | Coefficient of restitution, from 0 to 1. |
| v₁, v₂ | Final velocities, in metres per second (signed). |
The 2 kg body slows to 1 m/s and the 1 kg body leaves at 4 m/s. Momentum before and after both equal 6 kg·m/s.
Continue with the Displacement Calculator, Free Fall Calculator, or the Free Fall with Air Resistance Calculator — or browse more kinematics tools and all physics calculators.
It means no kinetic energy is lost to deformation, heat or sound. Real collisions sit below 1.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026