Coefficient of Restitution

e = \frac{v_2' - v_1'}{v_1 - v_2}

Ratio of relative speeds after and before collision. e=1 for elastic, e=0 for perfectly inelastic.

Variables

Coefficient of restitution

Measure of elasticity (0 to 1)

Allowed values: 0 to 1

unitless

v₂'

Final velocity of object 2

After collision

m/s

v₁'

Final velocity of object 1

After collision

m/s

v₁

Initial velocity of object 1

Before collision

m/s

v₂

Initial velocity of object 2

Before collision

m/s

Derivation

e = (relative speed of separation)/(relative speed of approach). Measures energy loss in collision.

Your notes

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Where this formula is listed

Mechanics formulas, under Momentum, alongside Impulse.
In the mechanics list it comes after Perfectly Inelastic Collision and before Angular Velocity.
Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Coefficient of Restitution formula?

Coefficient of Restitution is written e = (v₂′ − v₁′)/(v₁ − v₂). Ratio of relative speeds after and before collision. e=1 for elastic, e=0 for perfectly inelastic. It belongs to Mechanics, under Momentum.

What are the units in e = (v₂′ − v₁′)/(v₁ − v₂)?

In SI units, e is coefficient of restitution (dimensionless); v₂′ is final velocity of object 2, measured in m/s; v₁′ is final velocity of object 1, measured in m/s; v₁ is initial velocity of object 1, measured in m/s; v₂ is initial velocity of object 2, measured in m/s.

How is the Coefficient of Restitution formula derived?

e = (relative speed of separation)/(relative speed of approach). Measures energy loss in collision. The result is e = (v₂′ − v₁′)/(v₁ − v₂).