Case 1
- Drop height
- 1m
- Bounce height
- 0.6m
0.7746
Open with these valuesCoefficient of Restitution Calculator
0.7746e (0 to 1)
Result: 0.7746 e (0 to 1)Drop the ball from rest, measure how high it comes back, and take the square root of the ratio. A ball that returns to half its drop height has e ≈ 0.71, not 0.5 — the heights track energy while e compares speeds. The number is dimensionless and runs from 0 to 1.
Worked examples
Case 2
- Drop height
- 1m
- Bounce height
- 0.5m
0.7071
Open with these valuesCase 3
- Drop height
- 1.5m
- Bounce height
- 0.9m
0.7746
Open with these valuesHow it's calculated
e = √(h ÷ H)
- StepDrop the ball from rest and note the release height H.
- StepMeasure how high it rebounds after the first bounce, h, in the same unit.
- ResultRead e: 0 is a dead thud, 1 is a bounce that loses nothing.
Reference table
| Drop, bounce | What it is | e |
|---|---|---|
| 1, 0 | A beanbag — no rebound at all | 0 |
| 1, 0.5 | Back to half the drop height | 0.7071 |
| 1, 0.6 | About a tennis ball on a hard court | 0.7746 |
| 1, 1 | A perfectly elastic bounce | 1 |
| 1.5, 0.9 | The same ratio from a greater height | 0.7746 |
| 2, 0.5 | Back to a quarter of the drop height | 0.5 |
Questions
How do I calculate the coefficient of restitution?
Drop the object from rest, measure the bounce height, and take the square root of bounce divided by drop: e = √(h ÷ H). Both heights must use the same unit — 0.6 m back from 1 m gives √0.6 ≈ 0.7746.
What is the coefficient of restitution?
A dimensionless measure of how bouncy a collision is, the ratio of separation speed to approach speed. It runs from 0, a dead impact with no rebound, to 1, a perfectly elastic bounce that loses no energy. Every real material sits in between.
Why does the formula use a square root?
Because the heights track energy while e compares speeds, and speed goes with the square root of height. That is why a ball returning to half its drop height has e ≈ 0.71 rather than 0.5.
What is a typical value?
It depends on the pair of surfaces, not on the ball alone. A superball is around 0.9, a basketball about 0.75, a tennis ball near 0.7 and a baseball closer to 0.5. Clay or a beanbag sits near 0.
Can the bounce be higher than the drop?
Not in a passive bounce — the object cannot gain energy, so a result above 1 means the measurement or the units are wrong. Check that both heights use the same unit and that the ball was released from rest, not thrown.
Does gravity affect the result?
No. The same g appears in the fall and in the rebound and cancels out, so the drop test needs no value for it. The identical ball and floor would give the same e on the Moon.
Sources and last check
Information, not professional advice.