Coefficient of Restitution Calculator
Measure the bounciness of a collision from drop and bounce heights, and read off the impact and rebound speeds.
How it works
e = √(bounce height ÷ drop height) · impact speed = √(2g·h_drop) · rebound speed = √(2g·h_bounce) · KE retained = e²
The coefficient of restitution rates how elastic a bounce is, from 0 for a perfectly inelastic hit that sticks to 1 for a perfect elastic rebound that loses no energy. For a ball dropped onto a fixed surface it equals the ratio of rebound speed to impact speed, which — because speed after a fall is √(2gh) — simplifies to √(h_bounce/h_drop). Since kinetic energy scales with speed squared, the fraction of energy kept is exactly e².
Worked example
A ball dropped from 2 m rebounds to 1.5 m. e = √(1.5 / 2) = √0.75 ≈ 0.866. It hits at √(2 × 9.81 × 2) ≈ 6.26 m/s and leaves at √(2 × 9.81 × 1.5) ≈ 5.43 m/s, retaining e² = 75% of its kinetic energy.
Frequently asked questions
What values can the coefficient of restitution take?
Between 0 and 1 for ordinary collisions. e = 1 is a perfectly elastic bounce with no energy lost; e = 0 is perfectly inelastic, where the object does not rebound at all. A value above 1 would mean energy was added, which does not happen in a passive drop.
Why can I use heights instead of measuring speed?
Both impact and rebound speeds come from √(2gh), so gravity and the square roots cancel when you take the ratio. That leaves e = √(h_bounce / h_drop), which needs only two easy height measurements.
How much energy does a bounce lose?
The fraction kept is e², so the fraction lost is 1 − e². A ball with e = 0.866 keeps 75% and loses 25% of its kinetic energy to heat, sound and deformation on each bounce.
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This calculator is for educational purposes. Double-check important results before acting on them.