How to use the elastic collision calculator
Find the final velocities of two objects after a perfectly elastic collision. Enter mass 1, velocity 1, mass 2, velocity 2 in the fields above; the final velocity 1, final velocity 2, total kinetic energy are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- m1 — Mass 1 (kg)
- v1 — Velocity 1 (m/s)
- m2 — Mass 2 (kg)
- v2 — Velocity 2 (m/s)
Worked example
With mass 1 = 2 kg, velocity 1 = 5 m/s, mass 2 = 3 kg, velocity 2 = -1 m/s, the calculator gives final velocity 1 ≈ -2.2 m/s; final velocity 2 ≈ 3.8 m/s; total kinetic energy ≈ 26.5 J.
Frequently asked questions
What is the formula for the elastic collision calculation?
Final velocity 1 (m/s) = ((m1-m2) × v1+2 × m2 × v2) / (m1+m2). Final velocity 2 (m/s) = ((m2-m1) × v2+2 × m1 × v1) / (m1+m2). Total kinetic energy (J) = 0.5 × m1 × v1 × v1+0.5 × m2 × v2 × v2. Here m1 is mass 1 (kg), v1 is velocity 1 (m/s), m2 is mass 2 (kg), v2 is velocity 2 (m/s).
What inputs do I need for the elastic collision calculator (1d) calculator?
You need mass 1 in kg, velocity 1 in m/s, mass 2 in kg, velocity 2 in m/s. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.