Elastic Collision Calculator
The velocities after a head-on collision — elastic, inelastic or anywhere between — with the momentum and energy accounting.
Momentum is always conserved.
How the elastic collision calculator works
Momentum is always conserved. Kinetic energy is conserved only in a perfectly elastic collision, and the coefficient of restitution measures where a real collision sits: 1 is perfectly elastic, 0 is perfectly inelastic and the bodies move off together.
The classic result is that equal masses in an elastic head-on collision simply swap velocities — which is what the row of Newton's-cradle balls is demonstrating.
Formula: momentum conserved; e = separation speed / approach speed
Worked examples
| Inputs | Velocity 1 after (m/s) | Note |
|---|---|---|
| A 2 kg into a 3 kg | -3.4 | elastic — energy conserved |
| Perfectly inelastic | 0.8 | they move off together |
| Equal masses | -2 | they swap velocities exactly |
FAQFrequently asked questions
What is conserved in a collision?
Momentum, always. Kinetic energy only when the collision is perfectly elastic, which almost nothing real is.
What is the coefficient of restitution?
The ratio of separation speed to approach speed. One is perfectly elastic, zero means they stick together, and real materials sit between.
Why do equal masses swap velocities?
It is the only solution that conserves both momentum and kinetic energy when the masses match. Newton's cradle is a demonstration of exactly this.
Where does the lost energy go?
Heat, sound and permanent deformation. It is not destroyed — it just stops being kinetic.
Does this work in two dimensions?
No. This is the head-on case. A glancing collision needs the impact angle and splits the momentum into components.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.