Coefficient Of Restitution Calculator

Work out coefficient of restitution instantly with clear inputs, formula shown and shareable results.

About Coefficient Of Restitution Calculator

The coefficient of restitution is the ratio of rebound speed to impact speed, and since drop speed goes as the square root of height, it is the square root of the height ratio. Dropping from 1.5 m and bouncing to 0.9 m gives e = 0.775, retaining 60% of the energy. A value of 1 would be perfectly elastic and 0 a dead drop.

Formulas

From heights

e = sqrt(rebound height / drop height)

Energy retained

fraction = e^2 = h2 / h1

Worked example

With the default values below, Coefficient Of Restitution Calculator returns Coefficient Of Restitution of 0.7746. Change any input above and every figure here is recalculated in your browser.

Inputs used

Drop heightminimum 0 m: 1.5 m
Rebound heightminimum 0 m: 0.9 m

Results

Coefficient Of Restitution: 0.7746
Energy Retained In The Bounce: 60.00%
Impact Speed: 5.424 m/s
Rebound Speed: 4.201 m/s

Step by step

1Values used
2From heights
3Energy retained
4Coefficient Of Restitution= 0.7746
5Energy Retained In The Bounce= 60.00
6Impact Speed= 5.424 m/s
7Rebound Speed= 4.201 m/s

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What are typical values?

About 0.85 for a superball, 0.75 for a basketball, 0.6 for a tennis ball and near 0.1 for a beanbag.

Why is energy retention the square of e?

Because energy goes with speed squared, so a restitution of 0.8 keeps 64% of the energy.