Inelastic Collision Calculator
A perfectly inelastic collision — two objects that collide and move off together — with the shared final velocity, the kinetic energy before and after, and how much was lost to deformation, heat and sound.
Momentum is conserved in every collision, so the combined mass moves at (m₁u₁ + m₂u₂) ÷ (m₁ + m₂).
How the inelastic collision calculator works
Momentum is conserved in every collision, so the combined mass moves at (m₁u₁ + m₂u₂) ÷ (m₁ + m₂). Kinetic energy is not: sticking together destroys the largest possible share, which goes into crumpling and heat. Velocities are signed, so enter one of a head-on pair as negative.
Formula: v = (m₁u₁ + m₂u₂) ÷ (m₁ + m₂); ΔKE = KE_before − ½(m₁ + m₂)v²
Worked examples
| Inputs | Final velocity (m/s) | Note |
|---|---|---|
| 1,000 kg at 20 m/s hits a stationary 1,500 kg | 8 | 8 m/s; 120 kJ lost (60%) |
| Head-on: 1,000 kg at 15 and 1,000 kg at −15 | 0 | both stop; all energy lost |
| A 0.15 kg ball caught by a 60 kg skater at rest | 0.0748 | 0.075 m/s |
FAQFrequently asked questions
Why is energy lost but momentum not?
Momentum conservation follows from Newton’s third law and holds whatever the objects do to each other. Kinetic energy can turn into other forms — bent metal, heat, sound — and in a sticking collision the maximum possible share does.
What fraction is lost?
For a moving mass hitting a stationary one, the fraction lost is m₂ ÷ (m₁ + m₂): a car hitting a stationary lorry loses most of its energy; a lorry hitting a stationary car loses little of its own.
How do I enter a head-on collision?
Give the two objects opposite signs — 20 and −15, say. A negative final velocity means the pair moves in the second object’s original direction.
What about a partly elastic collision?
Real collisions sit between perfectly elastic and perfectly inelastic; the coefficient of restitution calculator handles those. The perfectly inelastic case is the lower bound on the energy that survives.
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.