Coefficient of Restitution Calculator
The coefficient of restitution — how elastic a collision is — from the speeds before and after, or from how high a ball bounces back, with the energy retained and the height of the next bounce.
The coefficient e is the ratio of separation speed to approach speed: 1 for a perfectly elastic collision, 0 for one where the objects stick.
How the coefficient of restitution calculator works
The coefficient e is the ratio of separation speed to approach speed: 1 for a perfectly elastic collision, 0 for one where the objects stick. For a ball dropped onto a hard floor it is simpler still, e = √(h_bounce ÷ h_drop), because kinetic energy at impact is proportional to height. Each bounce keeps e² of the energy.
Formula: e = (v₂ − v₁) ÷ (u₁ − u₂); or e = √(h₂ ÷ h₁)
Worked examples
| Inputs | Coefficient of restitution | Note |
|---|---|---|
| Dropped from 1 m, bounces to 0.64 m | 0.8 | e = 0.8 |
| Speeds: 5 and 0 before, 1 and 4 after | 0.6 | e = 0.6 |
| Basketball: 1.8 m to 1.35 m | 0.866 | e = 0.866 |
FAQFrequently asked questions
What are typical values?
Superball 0.9, basketball 0.85 (on a hard floor), golf ball 0.8, tennis ball 0.7, cricket ball 0.3–0.5, a lump of clay 0. Sports bodies specify e for balls — a basketball must bounce to 49–54 inches from 72.
Why the square root in the height version?
Speed at impact is √(2gh), so the ratio of speeds is the square root of the ratio of heights. Equivalently, e² is the fraction of energy the ball keeps.
Does it depend on the surface?
Yes — it is a property of the pair, not the ball alone. The same ball bounces higher on concrete than on grass, and e usually falls as impact speed rises.
How can I measure it at home?
Drop a ball from a measured height onto a hard floor, film it, and read the bounce height at the top of the first bounce. Repeat a few times and average.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.