Elastic Collision Calculator
Work out elastic collision instantly with clear inputs, formula shown and shareable results.
About Elastic Collision Calculator
A perfectly elastic collision conserves both momentum and kinetic energy, and solving the pair of equations gives the standard result for each final velocity. With 2 kg at 6 m/s meeting 3 kg at -2 m/s, the first rebounds at -3.6 m/s and the second moves off at 4.4 m/s. Momentum and energy totals are printed so you can confirm nothing was lost.
Formulas
First body
v1 = ((m1 - m2)u1 + 2 m2 u2) / (m1 + m2)
Second body
v2 = ((m2 - m1)u2 + 2 m1 u1) / (m1 + m2)
Worked example
With the default values below, Elastic Collision Calculator returns Final Velocity Of The First Body of -3.6000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Mass of the first bodyminimum 0 kg
- 2 kg
- Velocity of the first body
- 6 m/s
- Mass of the second bodyminimum 0 kg
- 3 kg
- Velocity of the second body
- -2 m/s
Results
- Final Velocity Of The First Body
- -3.6000 m/s
- Final Velocity Of The Second Body
- 4.4000 m/s
- Total Momentum (Unchanged)
- 6.000 kg m/s
- Total Kinetic Energy (Unchanged)
- 42.000 J
Step by step
- 1Values used
- 2First body
- 3Second body
- 4Final Velocity Of The First Body= -3.6000 m/s
- 5Final Velocity Of The Second Body= 4.4000 m/s
- 6Total Momentum (Unchanged)= 6.000 kg m/s
- 7Total Kinetic Energy (Unchanged)= 42.000 J
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What happens when the masses are equal?
They swap velocities exactly - the basis of the classic billiard-ball result and of Newton's cradle.
Are real collisions ever elastic?
Only approximately. Hard steel balls and gas molecules come close; anything that makes a noise or deforms has lost energy.