About this tool
Collision Calculator (1D) is a free, in-browser physics tool that finds the velocities after a head-on collision between two bodies. Enter each mass and initial velocity, choose the collision type, and it returns both final velocities plus the momentum and kinetic-energy accounting. All math runs locally in your browser.
Momentum is always conserved: p = m₁v₁ + m₂v₂. For a perfectly inelastic collision the bodies stick together at v' = (m₁v₁ + m₂v₂)/(m₁ + m₂). For an elastic collision it uses v₁' = ((m₁ − m₂)v₁ + 2m₂v₂)/(m₁ + m₂) and v₂' = ((m₂ − m₁)v₂ + 2m₁v₁)/(m₁ + m₂). For a custom coefficient of restitution e it combines momentum conservation with e = (v₂' − v₁')/(v₁ − v₂).
The result tiles show both post-collision velocities, the conserved total momentum, and the kinetic energy before and after so you can see exactly how much energy the collision dissipates. Use positive and negative velocities to indicate direction along the line of motion.
Frequently asked questions
What is the coefficient of restitution?
It is e = (v₂' − v₁')/(v₁ − v₂), the ratio of relative speed after to before the collision. e = 1 is perfectly elastic (no energy lost), e = 0 is perfectly inelastic (bodies stick), and values in between model real, partially bouncy collisions.
Is momentum always conserved?
Yes. Total momentum p = m₁v₁ + m₂v₂ is conserved in every collision type, which is why the momentum tile is identical before and after. Kinetic energy, by contrast, is only conserved in a perfectly elastic collision.
Why do equal masses swap velocities in an elastic collision?
When m₁ = m₂ the elastic formulas reduce to v₁' = v₂ and v₂' = v₁, so the two bodies simply exchange velocities — a classic result you can verify with equal masses and any speeds.
How should I enter directions?
Use the sign of each velocity: positive one way, negative the other along the line of impact. Masses must be positive. Everything is computed in your browser and nothing is uploaded.
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