Elastic Collision Calculator

How it works

1. 1Enter the mass and initial velocity of each object. Positive velocities move right; negative move left.
2. 2The calculator converts inputs to SI and applies v₁′ = ((m₁−m₂)u₁ + 2m₂u₂) ÷ (m₁+m₂) and v₂′ = ((m₂−m₁)u₂ + 2m₁u₁) ÷ (m₁+m₂).
3. 3Results are shown in your unit system. A positive value continues in the original direction; negative means it rebounded.

Use cases

• Physics students verifying billiard-ball or air-track collision problems.
• Engineers modelling impacts where deformation is negligible and energy loss is minimal.
• Game developers checking projectile collision physics against analytical solutions.

Frequently asked questions

What are the formulas used?

v₁′ = ((m₁−m₂)u₁ + 2m₂u₂) ÷ (m₁+m₂) and v₂′ = ((m₂−m₁)u₂ + 2m₁u₁) ÷ (m₁+m₂). They come from solving conservation of momentum and conservation of kinetic energy simultaneously.

What happens when both objects have the same mass?

When m₁ = m₂ the formulas simplify to v₁′ = u₂ and v₂′ = u₁ — the objects swap velocities. This is the Newton’s cradle result: a moving ball stops and the struck ball moves off at the original speed.

Can you walk through a worked example?

Let m₁ = 2 kg, u₁ = 3 m/s, m₂ = 1 kg, u₂ = 0. Sum = 3. v₁′ = ((2−1)×3 + 0) ÷ 3 = 1 m/s. v₂′ = (0 + 2×2×3) ÷ 3 = 4 m/s. Momentum before = 6, after = 2×1 + 1×4 = 6 ✓; KE before = 9 J, after = 1 + 8 = 9 J ✓.