Elastic Collision Calculator

A perfectly elastic collision is one in which both momentum and kinetic energy are conserved. No energy is lost to heat, sound, or deformation. This is common at the atomic and subatomic level, and is a useful approximation for collisions between hard objects like billiard balls.

In an elastic collision, total kinetic energy is conserved along with momentum. In an inelastic collision, momentum is still conserved but some kinetic energy is converted to other forms (heat, sound, deformation). A perfectly inelastic collision is one where the two objects stick together after impact.

The calculator uses two equations simultaneously: conservation of momentum (m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂) and conservation of kinetic energy (½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂²). Solving these gives: v₁ = ((m₁−m₂)u₁ + 2m₂u₂) / (m₁+m₂) and v₂ = ((m₂−m₁)u₂ + 2m₁u₁) / (m₁+m₂).

Yes. Negative velocities represent motion in the opposite direction. For example, if Object 1 moves to the right at 10 m/s and Object 2 moves to the left at 5 m/s, you would enter +10 for v₁ and −5 for v₂. The calculator handles signed values correctly.

When two objects of equal mass collide elastically in a head-on collision, they exchange velocities. Object 1 takes on the speed of Object 2, and vice versa. This is a classic result and a useful sanity check for the equations.

For a perfectly elastic collision, kinetic energy should be exactly conserved. Any tiny discrepancy in this calculator is purely due to floating-point rounding in the display. The underlying formula guarantees energy conservation by definition.

This calculator is designed for 1D (head-on) elastic collisions. For 2D collisions, you need to decompose velocities into x and y components and apply the elastic collision equations separately to each axis, which requires additional angle inputs.

The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. For two colliding objects, the combined momentum before the collision equals the combined momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.