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Coefficient of Restitution

e=v2−v1u1−u2e = \frac{v_2 - v_1}{u_1 - u_2}
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Worked example: Approach 10 m/s, separate 4 m/s → e = 0.4. Press Try an example to run it live, then adjust anything.

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Bounce Height from Coefficient of RestitutionCushion Rebound AngleCushion Rebound SpeedBank Shot Rail Contact Point
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See also

Conservation of Momentum (Two Bodies): Both use initial velocity and final velocity.Elastic Collision: Final Velocity of Body 1: Both use initial velocity and final velocity.Perfectly Inelastic Collision: Both use initial velocity and final velocity.Bounce Height from Coefficient of Restitution: Both use coefficient of restitution.Bank Shot Rail Contact Point: Both use coefficient of restitution.Cushion Rebound Angle: Both use coefficient of restitution.
1 more relatedCushion Rebound Speed: Both use coefficient of restitution.
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Coefficient of Restitution explained

u1u2v1v2e

Newton's experimental law of restitution says the relative speed after a collision is a fixed fraction of the relative speed before: e = separation ⁄ approach. e = 1 is perfectly elastic, e = 0 is perfectly inelastic (the bodies move off together), and everything real lands in between. Newton reported measurements in the Principia itself, swinging pendulum balls together and recording roughly 5/9 for glass and 15/16 for tightly wound wool.

Sports bodies now legislate the number. A regulation basketball must return 1.2–1.4 m when dropped from 1.8 m onto hardwood, an e of about 0.85; a tennis ball tested per ITF rules comes in near 0.75; golf drivers are capped by a related "COR" limit of 0.83 to keep drives in the stadium. Two traps: e is not a property of one object but of the pair of surfaces, and it drops measurably at high impact speeds, which is why the test conditions are specified so precisely.

Coefficient of Restitution formula

e=v2−v1u1−u2e = \frac{v_2 - v_1}{u_1 - u_2}
Where
  • ee= Coefficient of restitution
  • u1u_1= Initial velocity 1 (m/s)
  • u2u_2= Initial velocity 2 (m/s)
  • v1v_1= Final velocity 1 (m/s)
  • v2v_2= Final velocity 2 (m/s)
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Momentum, impulse and collisions

7 formulasMomentum and impulse, the conservation law that links two bodies, and the elastic, inelastic and restitution results for what happens after they meet.

Revised 31 October 2026
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formula.expert. (2026, October 31). Coefficient of Restitution Formula & Calculator. https://formula.expert/solvers/coefficient-of-restitution

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