Momentum Calculator
Use single-body mode for p = mv. For a head-on collision on a line, enter both masses and velocities (negative means the opposite direction) and choose elastic (bounce) or perfectly inelastic (stick together).
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Formula
- Momentum:
p = m × v - Elastic collision (1-D):
v1' = ((m1 − m2) × v1 + 2 × m2 × v2) ÷ (m1 + m2)andv2' = ((m2 − m1) × v2 + 2 × m1 × v1) ÷ (m1 + m2) - Perfectly inelastic collision:
v' = (m1 × v1 + m2 × v2) ÷ (m1 + m2)
Velocity is signed: choose one direction as positive and give bodies moving the other way a negative value. Inputs are converted exactly (1 lb = 0.45359237 kg, 1 mph = 0.44704 m/s, 1 km/h = 1/3.6 m/s) and answers are in SI units.
Worked example
A 2 kg body at 3 m/s hits a 1 kg body at rest.
- Total momentum = 2 × 3 + 1 × 0 = 6 kg·m/s
- Elastic: v1' = (1 × 3) ÷ 3 = 1 m/s, v2' = (2 × 2 × 3) ÷ 3 = 4 m/s. Check: 2 × 1 + 1 × 4 = 6, and the energy stays 9 J.
- Perfectly inelastic: v' = 6 ÷ 3 = 2 m/s. Energy after = ½ × 3 × 2² = 6 J, so 3 J is lost as heat and deformation.
Frequently asked questions
What is the momentum formula?
Momentum is mass times velocity, p = m × v, in kg·m/s. A 70 kg runner at 5 m/s has p = 350 kg·m/s. Velocity has a direction, so moving the opposite way gives −350.
How do I find final velocities in an elastic collision?
Both momentum and kinetic energy are conserved: v1' = ((m1 − m2)v1 + 2m2v2) ÷ (m1 + m2) and v2' = ((m2 − m1)v2 + 2m1v1) ÷ (m1 + m2). A 2 kg body at 3 m/s hitting a 1 kg body at rest leaves at 1 m/s and sends the other away at 4 m/s.
What is a perfectly inelastic collision?
The bodies stick together and move off with v = (m1v1 + m2v2) ÷ (m1 + m2). Momentum is conserved but kinetic energy is not: 2 kg at 3 m/s joining 1 kg at rest gives 2 m/s, and the energy drops from 9 J to 6 J.
Is momentum conserved in a collision?
Yes, whenever no outside force acts during the impact. In the example above the total momentum is 6 kg·m/s before and 3 × 2 = 6 kg·m/s after. Only the kinetic energy changes between the two collision types.
How do I enter bodies moving toward each other?
Give one body a negative velocity. A 1 kg body at 4 m/s meeting a 3 kg body at −2 m/s has total momentum 4 − 6 = −2 kg·m/s; if they stick, they move at −2 ÷ 4 = −0.5 m/s.