# Elastic Collision Calculator

Calculate final velocities for a 1D elastic collision. Verify kinetic energy and momentum conservation. Enter masses and initial velocities for instant.

## What this calculates

In a perfectly elastic collision, both kinetic energy and momentum are conserved. Given two objects' masses and initial velocities, this calculator determines their final velocities after a one-dimensional elastic collision and verifies the conservation laws.

## Inputs

- **Mass 1 (m₁)** (kg) — min 0.001 — Mass of the first object.
- **Velocity 1 (v₁)** (m/s) — Initial velocity of the first object (positive = rightward).
- **Mass 2 (m₂)** (kg) — min 0.001 — Mass of the second object.
- **Velocity 2 (v₂)** (m/s) — Initial velocity of the second object (negative = leftward).

## Outputs

- **Final Velocity 1 (v₁')** (m/s) — Velocity of object 1 after the collision.
- **Final Velocity 2 (v₂')** (m/s) — Velocity of object 2 after the collision.
- **Kinetic Energy Conserved?** — formatted as text — Verification that total kinetic energy is conserved.
- **Momentum Conserved?** — formatted as text — Verification that total momentum is conserved.

## Details

An elastic collision is one in which the total kinetic energy of the system is conserved (no energy is lost to heat, sound, or deformation). The conservation of both momentum and kinetic energy yields two equations that can be solved simultaneously for the two final velocities:

v1f = ((m1 - m2)v1 + 2m2v2) / (m1 + m2)
v2f = ((m2 - m1)v2 + 2m1v1) / (m1 + m2)

Special cases are instructive: when two equal masses collide, they exchange velocities. When a small object bounces off a much larger stationary one, the small object reverses direction at nearly the same speed. When a large object hits a small stationary one, the small one flies off at nearly twice the large object's speed. True elastic collisions occur in atomic and subatomic physics; macroscopic collisions always lose some energy to deformation and heat.

## Frequently Asked Questions

**Q: What is the difference between elastic and inelastic collisions?**

A: In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not. Some is converted to heat, sound, or deformation. A perfectly inelastic collision is one where the objects stick together.

**Q: Do perfectly elastic collisions exist in real life?**

A: At the macroscopic level, no collision is perfectly elastic; some energy is always lost. However, collisions between billiard balls and steel balls are close. At the atomic level, collisions between noble gas atoms and in particle physics are truly elastic.

**Q: What happens when equal masses collide elastically?**

A: They exchange velocities. If a moving ball hits an identical stationary ball, the first stops completely and the second moves off at the original speed. This is demonstrated beautifully by Newton's cradle.

**Q: Can this calculator handle head-on collisions?**

A: Yes. Use positive velocity for rightward motion and negative for leftward. Head-on collisions are simply cases where the two velocities have opposite signs.

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Source: https://vastcalc.com/calculators/physics/elastic-collision
Category: Physics
Last updated: 2026-04-21