Collision Calculator
The speeds after a collision, elastic, inelastic or anywhere in between, with the energy that survives and the energy that does not.
Results
What this tool does
Two things hit each other, and what happens next is decided by one number: how bouncy the contact is. At one extreme nothing is lost and they part as fast as they met; at the other they stick together and move off as one. Everything real happens in between. Put in the two masses, the two speeds before, and how elastic the collision is, and this page gives the speeds after, the momentum (which never changes) and the kinetic energy (which usually does) — so you can see exactly how much of the motion was converted into heat and noise.
Formula
v₁ = (p + m₂ e (u₂ − u₁)) ÷ (m₁ + m₂) · v₂ = (p + m₁ e (u₁ − u₂)) ÷ (m₁ + m₂), p = m₁u₁ + m₂u₂
Variables
| Symbol | Meaning | Unit |
|---|---|---|
m1 | First mass | kg |
u1 | Speed of the first before | m/s |
m2 | Second mass | kg |
u2 | Speed of the second before | m/s |
mode | Kind of collision | — |
restitution | Coefficient of restitution | — |
V1 | Speed of the first after | m/s |
V2 | Speed of the second after | m/s |
MO | Total momentum, before and after | kg·m/s |
EB | Kinetic energy before | J |
EA | Kinetic energy after | J |
EL | Energy turned into heat and noise | J |
EP | Share of the energy lost | % |
KD | Kind of collision | — |
CS | How fast they approached | m/s |
SS | How fast they part | m/s |
CV | Speed of the centre of mass | m/s |
RE | Coefficient of restitution | — |
Worked example
- First mass2 kg
- Speed of the first before5 m/s
- Second mass3 kg
- Speed of the second before0 m/s
- Kind of collisionelastic
- Coefficient of restitution0.5
- Speed of the first after-1.000000 m/s
- Speed of the second after4.000000 m/s
- Total momentum, before and after10.000000 kg·m/s
- Kinetic energy before25.000000 J
- Kinetic energy after25.000000 J
- Energy turned into heat and noise0.000000 J
- Share of the energy lost0.0000 %
- Kind of collisionElastic — they bounce apart, nothing lost
- How fast they approached5.000000 m/s
- How fast they part5.000000 m/s
- Speed of the centre of mass2.000000 m/s
- Coefficient of restitution1.0000
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
Frequently asked questions
What does the coefficient of restitution mean?
How much of the approach speed survives as separation speed. At 1 the two objects part exactly as fast as they came together and no energy is lost — that is an elastic collision, and only things like billiard balls come close. At 0 they do not separate at all and move off together, which is perfectly inelastic. Real collisions sit in between: a basketball on concrete is around 0.8, a tennis ball about 0.7, and a car crumple zone is deliberately designed to be near zero, because energy that goes into deforming metal is energy that does not go into the people inside.
Why is momentum always conserved but energy is not?
Because during the collision the two objects push on each other with equal and opposite forces for exactly the same length of time, so whatever momentum one gains the other loses. That holds no matter how messy the contact is. Energy has no such guarantee: it can leave the motion entirely and reappear as heat in bent metal, as sound, or as permanent deformation, and none of that comes back. Check the two figures above — the momentum before and after are the same in every mode, while the energy is only equal when the collision is perfectly elastic.