What is a perfectly elastic collision?

A perfectly elastic collision is one in which both momentum and kinetic energy are conserved. No energy is lost to heat, sound, or deformation. Billiard balls and atomic particles approximate this behavior.

What formulas does this calculator use?

Final velocity of object 1: v1' = ((m1-m2)·u1 + 2·m2·u2) / (m1+m2). Final velocity of object 2: v2' = ((m2-m1)·u2 + 2·m1·u1) / (m1+m2). These are derived from simultaneous conservation of momentum and kinetic energy.

Can I enter negative velocities?

Yes. Positive velocity means the object moves to the right; negative means it moves to the left. This lets you model head-on collisions by giving one object a negative initial velocity.

What happens when masses are equal?

When m1 = m2, the objects exchange velocities. Object 1 takes on the initial velocity of Object 2 and vice versa. This is easy to verify with billiard balls.

What is the difference between elastic and inelastic collisions?

In an elastic collision, kinetic energy is conserved. In an inelastic collision, some kinetic energy is converted to other forms of energy. A perfectly inelastic collision is when the objects stick together after impact.

Elastic Collision Calculator

Name: Elastic Collision Calculator
Availability: InStock
Author: Nham Vu

Enter masses and initial velocities to instantly compute final velocities after a perfectly elastic 1D collision.

Collision Parameters

Object 1

Mass (kg)

Initial Velocity (m/s)

Object 2

Mass (kg)

Initial Velocity (m/s)

Positive velocity = moving right. Negative = moving left.

Enter masses and velocities, then click Calculate.

Final Velocities

Object 1

—

m/s

Object 2

—

m/s

Conservation Check

Quantity	Before	After	Conserved
Momentum (kg·m/s)	—	—	—
Kinetic Energy (J)	—	—	—

Direction Overview

Summary

Enter masses and initial velocities to instantly compute final velocities after a perfectly elastic 1D collision.

How it works

Enter the mass and initial velocity of Object 1 (positive = moving right).
Enter the mass and initial velocity of Object 2.
Click Calculate to apply the elastic collision formulas.
View the final velocities, momentum, and kinetic energy for both objects.
Use the Swap button to quickly reverse the scenario.
Adjust any value and recalculate to explore different collision outcomes.

Use cases

Verify homework and exam answers for introductory physics courses.
Demonstrate conservation laws in classroom or lab settings.
Model billiard ball or Newton's cradle mechanics.
Explore how mass ratio affects post-collision velocities.
Check game physics engines for elastic collision behavior.
Understand equal-mass collisions where velocities exchange.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu