Calculate final velocities after elastic or perfectly inelastic collisions using the law of conservation of momentum. Enter the mass and initial velocity of each object, choose the collision type, and the calculator shows final velocities, total momentum, kinetic energy before and after, and energy lost.
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Standard physics formula
Law of conservation of momentum; elastic and perfectly inelastic collision equations.
1. Object 1
kg
m/s
2. Object 2
kg
m/s
Please enter valid numbers for all fields. Masses must be greater than zero.
Collision Results
Final velocity (obj 1)
-
m/s after collision
Final velocity (obj 2)
-
m/s after collision
Total momentum
-
kg m/s (conserved)
Kinetic energy lost
-
joules
Momentum Breakdown
Momentum of object 1 (before)-
Momentum of object 2 (before)-
Total momentum (before)-
Momentum of object 1 (after)-
Momentum of object 2 (after)-
Total momentum (after)-
Kinetic Energy Breakdown
KE of object 1 (before)-
KE of object 2 (before)-
Total KE (before)-
KE of object 1 (after)-
KE of object 2 (after)-
Total KE (after)-
Energy change-
Summary:Enter values above to see results.
How Conservation of Momentum Works
The law of conservation of momentum is a fundamental principle of classical physics. It states that in a closed system (one with no external forces such as friction or gravity acting along the direction of motion), the total momentum before a collision equals the total momentum after the collision.
Momentum (p) is the product of mass and velocity:
p = m × v
where m is mass in kilograms and v is velocity in metres per second. Because velocity has direction, momentum is a vector. Velocities (and momenta) to the right are positive by convention; velocities to the left are negative.
Collision Types Explained
Collision Type
Momentum
Kinetic Energy
What Happens
Elastic
Conserved
Conserved
Objects bounce off; no energy lost to heat or deformation
Perfectly inelastic
Conserved
Not conserved (maximum loss)
Objects stick together and move as one mass
Inelastic (general)
Conserved
Partially lost
Objects bounce off but some energy is dissipated
This calculator handles elastic and perfectly inelastic collisions. Real-world collisions (such as a car crash or a ball bouncing on a floor) are typically partially inelastic, falling between the two extremes.
Formulas Used
Elastic collision (momentum and kinetic energy both conserved). Solving the two simultaneous equations gives the standard result:
Sources and method: Newton's laws of motion and the law of conservation of momentum (classical mechanics). Elastic collision equations derived from simultaneous solution of conservation of momentum (m1v1i + m2v2i = m1v1f + m2v2f) and conservation of kinetic energy (0.5m1v1i² + 0.5m2v2i² = 0.5m1v1f² + 0.5m2v2f²). Reference: Halliday, Resnick and Krane, Physics (5th ed.), Chapters 9 and 10.
This calculator uses idealised one-dimensional collision models. Real-world collisions may involve friction, deformation, angular momentum, or forces in multiple dimensions not captured here. For accurate engineering calculations, consult a qualified engineer or physicist.
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