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Momentum Calculator
Solve the momentum equation p = mv for any variable, or switch to impulse to find J = F·Δt and the change in momentum from a collision or push. Units for mass, speed, force and time are converted for you.
Calculate
Use a negative value for the opposite direction.
Enter your values to see the result.
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How to use the Momentum Calculator
- Pick what to calculate: momentum, mass, velocity, impulse or momentum change.
- Enter the known values and choose a unit for each one.
- Use negative velocities for motion in the opposite direction, for example a ball that bounces back.
- Add a contact time in Momentum change mode to get the average force of the impact.
- Read the result and the steps, then copy the results or download the table as CSV.
Momentum and impulse formulas
- Momentum: p = m × v, so m = p ÷ v and v = p ÷ m
- Impulse: J = F × Δt
- Impulse-momentum theorem: J = Δp = m × (v₂ − v₁)
- Average force: F = Δp ÷ Δt
- Kinetic energy from momentum: KE = p² ÷ (2m)
Example: a 1,500 kg car moving at 25 m/s has p = 1,500 × 25 = 37,500 kg·m/s. If it brakes to a stop in 4 s, the momentum change is −37,500 N·s and the average braking force is 37,500 ÷ 4 = 9,375 N.
Typical momentum values
| Object | Mass | Speed | Momentum (kg·m/s) |
|---|---|---|---|
| Tennis ball serve | 58 g | 50 m/s | 2.9 |
| Baseball pitch | 145 g | 40 m/s | 5.8 |
| Person walking | 70 kg | 1.4 m/s | 98 |
| Cyclist with bike | 85 kg | 7 m/s | 595 |
| Car in town | 1,500 kg | 14 m/s (50 km/h) | 21,000 |
| Loaded truck on highway | 30,000 kg | 25 m/s (90 km/h) | 750,000 |
Unit conversions
- 1 kg·m/s = 1 N·s = 100,000 g·cm/s
- 1 lb·ft/s = 0.138255 kg·m/s
- 1 lbf·s = 4.44822 N·s
Frequently asked questions
What is the formula for momentum?
Linear momentum is mass times velocity: p = m × v. In SI units mass is in kilograms and velocity in meters per second, so momentum is in kg·m/s, which is the same as newton-seconds (N·s).
What is impulse?
Impulse is force multiplied by the time it acts: J = F × Δt. By the impulse-momentum theorem it equals the change in momentum, J = Δp = m(v₂ − v₁). It is measured in N·s, the same unit as momentum.
Is momentum a vector?
Yes. Momentum has the same direction as the velocity. Use a positive value for one direction and a negative value for the opposite direction, which matters for rebounds: a ball going from −40 m/s to +50 m/s has a velocity change of 90 m/s.
How is momentum different from kinetic energy?
Momentum (mv) grows in proportion to speed and has a direction, while kinetic energy (½mv²) grows with the square of speed and has no direction. Doubling speed doubles momentum but quadruples kinetic energy. They are linked by KE = p² ÷ 2m.
How do I find the average force of an impact?
Divide the change in momentum by the contact time: F = Δp ÷ Δt. A longer stopping time, such as from airbags or crumple zones, means a smaller average force for the same momentum change.
Is momentum conserved?
In a closed system with no external forces, the total momentum before a collision equals the total momentum after it. Kinetic energy is only conserved in perfectly elastic collisions.
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