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Physics

Elastic Collision Calculator

Calculate both final velocities for an ideal one-dimensional elastic collision.

SI units shown beside each fieldIdeal model explained below
Collision lab
Collision lab

Use signed velocities along the same axis for both objects.

See the method

Set masses and initial velocities

Runs on your device

Final velocities

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter mass 1, initial velocity 1, mass 2, initial velocity 2.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

v1f=[(m1−m2)v1+2m2v2]/(m1+m2); v2f=[2m1v1+(m2−m1)v2]/(m1+m2).

A WORKED EXAMPLE

Using mass 1 = 2 kg, initial velocity 1 = 5 m/s, mass 2 = 3 kg, initial velocity 2 = 0 m/s, the result is -1 m/s. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Main result is final velocity 1. Perfectly elastic impact conserves momentum and kinetic energy; geometry must permit an actual collision.

What to keep in mind

Main result is final velocity 1. Perfectly elastic impact conserves momentum and kinetic energy; geometry must permit an actual collision. An idealized educational model using the stated SI units. Real systems may need additional forces, losses or experimental measurements. Not a safety or equipment specification.

Common questions

How do I use this elastic collision calculator?

Calculate both final velocities for an ideal one-dimensional elastic collision. Enter mass 1 in kg, initial velocity 1 in m/s, mass 2 in kg, initial velocity 2 in m/s. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Main result is final velocity 1. Perfectly elastic impact conserves momentum and kinetic energy; geometry must permit an actual collision.

Methodology maintained by ClarityKit. How these tools are built and checked.