Coefficient of Restitution Calculator
The coefficient of restitution tells you how much speed a bouncing object keeps through an impact. The simplest way to measure it is a drop test: drop an object from a known height and record how high it bounces. The square root of the height ratio is the coefficient of restitution. This calculator takes the drop height, the bounce height, and gravity, then returns the coefficient of restitution, the impact and rebound speeds, and the fraction of kinetic energy retained in the bounce.
Restitution drop-test formula
e = sqrt( bounce height / drop height )
Impact speed = sqrt( 2 * g * drop height )
Rebound speed = sqrt( 2 * g * bounce height )
Energy retained = 100 * e^2 = 100 * (bounce / drop)
Speeds come from energy conservation during the free fall and rise. The coefficient of restitution is the ratio of rebound to impact speed, which equals the square root of the height ratio.
Restitution facts
- e equals 1 for a perfectly elastic collision and 0 for a perfectly inelastic one.
- Energy retained in the bounce equals e squared.
- The bounce height can never exceed the drop height for a passive collision.
- A basketball is roughly 0.75 to 0.85; a tennis ball roughly 0.7.
- For most materials e falls slightly as impact speed rises.
Coefficient of restitution: frequently asked questions
What is the coefficient of restitution?
The coefficient of restitution, written e, measures how bouncy a collision is. It is the ratio of the separation speed to the approach speed. A perfectly elastic collision has e equal to 1, and a perfectly inelastic collision (no bounce) has e equal to 0. Most real collisions fall in between.
How is e found from a drop test?
When a ball is dropped from a height and bounces back, the coefficient of restitution equals the square root of the bounce height divided by the drop height. This works because the speed before and after impact is proportional to the square root of the corresponding height under gravity.
How much energy is retained in a bounce?
Kinetic energy scales with speed squared, and the speed ratio is e, so the fraction of kinetic energy retained after the bounce is e squared. The same fraction equals the bounce height divided by the drop height, since the height is proportional to the energy.
What is a typical coefficient of restitution?
Values depend on the materials and impact speed. A basketball is around 0.75 to 0.85, a tennis ball around 0.7, and a hard steel ball on steel can exceed 0.9. A lump of clay is close to 0. Enter your own measured heights for the exact value of your collision.
Does the coefficient of restitution depend on speed?
Yes, slightly. For many materials e decreases as impact speed rises because more energy goes into permanent deformation and heat. A drop test gives the value at that particular impact speed, so testing at a representative height is best.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.