ONE FORMULA, ONE ANSWER
Collision velocity with restitution calculator
Find the first body’s final velocity from linear momentum and the coefficient of restitution. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
First final velocity v₁
Enter values and select Calculate.
v₁ = [(m₁ − e m₂)u₁ + (1 + e)m₂u₂] / (m₁ + m₂)
Assumptions
Required: one-dimensional contact, negligible external impulse, and 0 ≤ e ≤ 1. Body 1 is behind body 2 along the positive axis, so u₁ ≥ u₂. Equal initial velocities give the unchanged limiting value. Excluded: oblique impact, rotation, and fragmentation.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
- OpenStax — one-dimensional inelastic collisions
- MIT OCW · One-dimensional collision and coefficient of restitution
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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