Elastic Collision Calculator

Solve a perfectly elastic one-dimensional impact

A perfectly elastic collision conserves both total momentum and total kinetic energy. This calculator uses the closed-form one-dimensional solution for two masses and two signed initial velocities, then reports each final velocity and checks the before-and-after momentum. It is useful for ideal particle problems, carts on a track, and sanity checks before simulating more complicated impacts.

With mass one equal to two kilograms moving at three meters per second and mass two equal to one kilogram at rest, final velocity one is one meter per second and final velocity two is 4 meters per second. Initial and final momentum are both 6 kilogram-meters per second, while kinetic energy remains 9 joules.

Use signed velocities and ideal assumptions

Positive and negative signs represent opposite directions on one axis. The model assumes a perfectly elastic, instantaneous, central collision with no rotation, deformation loss, friction, or external impulse. Computation stays in your browser. Real impacts usually have a coefficient of restitution below one, and oblique collisions require vector normal and tangential components rather than this scalar formula.