One Dimensional Elastic Collision

Solve final velocities for an isolated perfectly elastic collision.

Your numbers

Final A velocity

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Idealized classical model in SI units. Check sign conventions and assumptions; not a certified engineering design calculation.

Formula

Use vₐ = [(mₐ−mᵦ)uₐ+2mᵦuᵦ]/(mₐ+mᵦ) and vᵦ = [2mₐuₐ+(mᵦ−mₐ)uᵦ]/(mₐ+mᵦ). m denotes mass, u initial signed velocity, and v final signed velocity; subscripts distinguish the bodies. Use consistent mass and velocity units.

Solve final velocities for an isolated perfectly elastic collision.

Worked example

Mass A (kg): 2
Mass B (kg): 2
Initial A velocity (m/s): 5
Initial B velocity (m/s): 0

Final A velocity: 0 m/s
Final B velocity: 5 m/s

Scope and limitations

Idealized classical model in SI units. Check sign conventions and assumptions; not a certified engineering design calculation.

Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.

Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.

Formula version: c42d356aa4ab · Example checked: 2026-10-30

Methodology