Physics

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Physics

Collision Elasticity Calculator.

Calculates the coefficient of restitution for a collision between two objects, measuring how elastic the collision is.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Measure the relative velocity of the two objects just before collision.

  2. 2

    Measure the relative velocity just after collision.

  3. 3

    Divide the after velocity by the before velocity.

  4. 4

    The result is the coefficient of restitution (e).

relative_velocity_after / max(relative_velocity_before, 0.0001)

Frequently asked questions

What does a coefficient of restitution of 1 mean?

It means a perfectly elastic collision where kinetic energy is conserved and relative velocity is unchanged.

What does a coefficient of 0 mean?

It means a perfectly inelastic collision where objects stick together and relative velocity after is zero.

Can the coefficient be greater than 1?

In real collisions, no. Values above 1 would imply energy is gained, which is not physically possible.

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Coefficient of restitution

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How it works

Calculates the coefficient of restitution for a collision between two objects, measuring how elastic the collision is.

  1. Measure the relative velocity of the two objects just before collision.
  2. Measure the relative velocity just after collision.
  3. Divide the after velocity by the before velocity.
  4. The result is the coefficient of restitution (e).

Formulas

The math behind this calculator, written out so you can verify the result.

Coefficient of Restitution

e = v_after / v_before

The ratio of relative speed after collision to relative speed before collision.

Example:

Input: v_before = 10 m/s, v_after = 8 m/s

Calculation: e = 8 / 10

Result: e = 0.8

Real-world use cases

Where this calculation shows up in everyday life.

Sports equipment testing

Measure the bounce of a ball to ensure it meets regulations.

Example: A tennis ball must have a coefficient between 0.5 and 0.75.

Vehicle safety design

Evaluate crumple zones by measuring how much kinetic energy is absorbed.

Example: Lower e means more energy absorbed, safer for occupants.

Physics education

Demonstrate elastic and inelastic collisions in the classroom.

Example: Compare steel balls (e≈0.95) to clay (e≈0).

Tips and common mistakes

Tips

  • Use consistent units for both velocities.
  • Ensure velocities are measured along the same line.
  • For real collisions, e is between 0 and 1.
  • A perfectly elastic collision is an idealization.

Common Mistakes to Avoid

  • Using absolute speeds instead of relative velocities.
  • Forgetting that the after velocity can be zero.
  • Assuming e is always constant for a material.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.