🎱 Collision Calculator (1D)
Enter two masses and their initial velocities to get the final velocities after an elastic, inelastic or partially-elastic collision.
Final velocity v₁
1 m/s
Final velocity v₂
4 m/s
Momentum (conserved)
6 kg·m/s
KE before → after
9 → 9 J
Kinetic energy lost
0 J
Momentum is always conserved: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. In a perfectly elastic collision (e = 1) kinetic energy is also conserved; in a perfectly inelastic one (e = 0) the objects stick together and the most kinetic energy is lost to heat/sound. The coefficient of restitution e sets where between those a real collision falls. 🔒 In your browser.
How the collision calculator (1d) works
Momentum is conserved in every collision: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. That is one equation for two unknowns, so the second comes from the coefficient of restitution e, which sets how much relative speed survives the impact. The tool solves both together — e = 1 for a perfectly elastic collision (kinetic energy also conserved), e = 0 for a perfectly inelastic one (the objects stick together) — and reports the kinetic energy before, after and lost.
Velocities are signed: use a negative value for an object moving the opposite way. The elastic case is the one that trips people up, because it needs two conservation laws at once; a classic result is that equal masses simply exchange velocities. Real collisions sit between the extremes (0 < e < 1), losing some energy to heat, sound and deformation.
Frequently asked questions
How do I calculate final velocities in a collision?
Use conservation of momentum plus the collision type. For a perfectly elastic collision, v₁ = ((m₁−m₂)u₁ + 2m₂u₂)/(m₁+m₂) and v₂ = ((m₂−m₁)u₂ + 2m₁u₁)/(m₁+m₂). The tool handles elastic, inelastic and everything between.
What is the difference between elastic and inelastic collisions?
In an elastic collision both momentum and kinetic energy are conserved. In an inelastic one only momentum is conserved — some kinetic energy becomes heat, sound or deformation. Perfectly inelastic means the objects stick together afterward.
What is the coefficient of restitution?
A number e from 0 to 1 measuring how "bouncy" a collision is: the ratio of relative speed after to before. e = 1 is perfectly elastic, e = 0 is perfectly inelastic (they stick), and real collisions are in between.
What happens when two equal masses collide elastically?
They exchange velocities. If one is moving and the other still, the moving one stops and the other moves off at the first one's speed — the classic Newton's-cradle result.
Is momentum always conserved?
Yes, in any collision with no external forces — elastic or inelastic. Kinetic energy is only conserved in a perfectly elastic collision; otherwise some is lost, which the tool shows as the kinetic energy lost.