Momentum & Collision Calculator (Elastic, Inelastic, Coefficient of Restitution)
Calculate 1D collisions between two bodies. Supports perfectly elastic, perfectly inelastic, and coefficient-of-restitution collisions, comparing momentum and kinetic energy before and after impact.
Tips
- Both masses must be positive numbers. Velocities can be negative, which represents motion in the opposite direction.
- Setting e=1 in the "Coefficient of Restitution" mode reproduces the perfectly elastic result exactly, and e=0 reproduces the perfectly inelastic result exactly — a good way to see how the three modes connect.
- Total momentum always matches before and after the collision, regardless of collision type. This is simply the law of conservation of momentum for a closed system with no external force.
- Total kinetic energy is conserved only in a perfectly elastic collision; in inelastic collisions some of it is lost as heat, sound, or deformation. Check the "Kinetic energy lost" row to see how much.
- Car crash safety design deliberately favors inelastic-like deformation of the vehicle body to absorb impact energy and reduce the force transmitted to occupants.
Frequently Asked Questions
Side Note — Where Does the Coefficient of Restitution Come From?
The coefficient of restitution is often traced back to experiments by Isaac Newton in the 17th century, who dropped balls of various materials and measured how high they bounced back. He found that the ratio of relative velocities before and after impact stayed roughly constant for a given pair of materials — a discovery that, alongside the laws of motion, became a key tool for quantifying collisions.
Interestingly, while the coefficient always falls between 0 and 1, its exact value can shift slightly with impact speed and temperature even for the same pair of materials. This is because it behaves more like an empirical approximation of a material's elastic deformation properties than a strict physical law. Sports equipment regulations, such as those for baseballs and golf balls, specify tight bounds on the coefficient of restitution to keep equipment performance within fair limits.
A perfectly elastic collision (e=1) is a theoretical ideal that is essentially never achieved exactly at everyday, macroscopic scales — only at the atomic or molecular level does it become realistic. Billiard balls and the metal balls in a Newton's cradle come close, with only small amounts of energy escaping as sound and heat. At the other extreme, near-perfectly inelastic collisions (e≈0) include lumps of clay sticking together or a car crumpling to a stop against a wall.