Elastic Collision Calculator

An elastic collision is defined by two things surviving it: momentum and kinetic energy. That pair of conditions is enough to fix both final velocities exactly, with no other information needed. This computes them from the masses and initial velocities, then recomputes both quantities from the answer — so the conservation is demonstrated on your numbers rather than promised in the introduction.

First mass

Units do not matter as long as both masses use the same one.

Second mass

Equal masses simply exchange velocities, which is worth trying first.

First velocity

Positive is to the right; a negative value means it is moving left.

Second velocity

Set this to zero for the classic case of hitting something stationary.

Your result will appear here.

What this generator does

Applies the standard one-dimensional elastic collision formulas to your masses and velocities, then recomputes total momentum and total kinetic energy from the results and compares them against the values before the collision.

How to use this tool

Enter the two masses and the two velocities before the collision.
Use a negative velocity for a body moving the other way.
Read both velocities after the collision.
Check the momentum and energy figures: before and after must match.

Understanding the controls

The two masses: Any consistent units. What matters is the ratio: a very heavy body barely changes speed, however fast the light one hits it.
The two velocities: Positive is rightwards. Set the second to zero for the textbook case of striking something stationary, or make it negative for a head-on approach.

Common use cases

Checking a physics homework answer against an independent calculation
Exploring what happens when a light body hits a much heavier one
Teaching conservation laws with numbers a student can verify
Building worked examples for a mechanics lesson
Seeing why equal masses simply swap velocities

How this generator works

Conservation of momentum and conservation of kinetic energy give two equations in two unknowns, and solving them yields the standard formulas used here. Before display the tool recomputes total momentum and total kinetic energy from the final velocities and compares each against its value beforehand. It also checks an equivalent characterisation: in an elastic collision the speed at which the bodies separate equals the speed at which they approached, which is a genuinely different statement from the two conservation sums.

Randomness and fairness

Nothing here is random. Two masses and two velocities determine the outcome completely.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

One dimension only, so this is a head-on collision — glancing collisions need vectors and an impact parameter.
Perfectly elastic, meaning no energy goes into heat, sound or deformation; real collisions between everyday objects are never quite this.
No external forces during the collision, so friction and gravity are ignored for the instant it lasts.
Relativistic speeds are outside the model, which uses ordinary Newtonian mechanics throughout.

Privacy and your data

Both velocities are worked out in your browser. The masses and speeds you enter are never transmitted, stored or included in analytics.