Elastic Collision Calculator

About this calculator

For a head-on, one-dimensional elastic collision between two masses, both momentum (m₁v₁+m₂v₂) and kinetic energy are conserved, which together yield the closed-form final velocities v₁' = ((m₁−m₂)/(m₁+m₂))v₁ + (2m₂/(m₁+m₂))v₂ and v₂' = (2m₁/(m₁+m₂))v₁ + ((m₂−m₁)/(m₁+m₂))v₂. A useful check: if the two masses are equal, they simply swap velocities.

This model underlies introductory mechanics courses on collisions, but the same algebra describes billiard and pool ball strikes, gas molecule collisions in kinetic theory, and idealized particle-physics scattering where energy loss is negligible. Physics students, game and simulation programmers building realistic physics engines, and engineers doing first-pass estimates of near-elastic impacts (like steel ball bearings) all use this formula.