Momentum Calculator
Mass times velocity, impulse and impact force, and what happens when two objects collide, from a perfect bounce to a pile-up.
By Manzoor Ahmad, pharmacist · Updated How do you calculate momentum?
Momentum p = m × v. A 1,500 kg car moving at 20 m/s (72 km/h) has 1,500 × 20 = 30,000 kg·m/s of momentum. In a collision total momentum is conserved, and a change in momentum (impulse) equals the average force times the contact time.
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Momentum of everyday objects
| Object | Mass | Speed | Momentum |
|---|---|---|---|
| Baseball pitch | 0.145 kg | 40 m/s | 5.8 kg·m/s |
| Rifle bullet | 8 g | 900 m/s | 7.2 kg·m/s |
| Sprinter | 80 kg | 10 m/s | 800 kg·m/s |
| Car at 72 km/h | 1,500 kg | 20 m/s | 30,000 kg·m/s |
| Loaded truck at 90 km/h | 40,000 kg | 25 m/s | 1,000,000 kg·m/s |
A bullet and a baseball carry similar momentum, but the bullet’s kinetic energy is about 28 times larger (3,240 J vs 116 J), which is why momentum and kinetic energy tell different stories.
Collision formulas (1D)
- Conservation: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
- Restitution: v₂ − v₁ = e(u₁ − u₂)
- Combined: v₁ = [m₁u₁ + m₂u₂ + m₂e(u₂ − u₁)] ÷ (m₁ + m₂) and v₂ = [m₁u₁ + m₂u₂ + m₁e(u₁ − u₂)] ÷ (m₁ + m₂)
Momentum FAQs
Momentum p = m × v, mass times velocity. With mass in kilograms and velocity in m/s, momentum is in kg·m/s (equivalent to N·s).
Multiply mass by velocity. A 1,500 kg car at 20 m/s (72 km/h) has a momentum of 30,000 kg·m/s.
Yes. Momentum points in the direction of motion, so in one-dimensional problems use positive for one direction and negative for the other.
Impulse J is the change in momentum, J = Δp = m(v₂ − v₁), and it also equals average force times contact time, J = FΔt.
Divide the change in momentum by the contact time: F = m(v₂ − v₁) ÷ Δt. A 145 g baseball reversing from 40 m/s to 50 m/s in 1 ms feels about 13,000 N.
In a closed system with no external forces, total momentum before a collision equals total momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
Both conserve momentum. Elastic collisions also conserve kinetic energy (billiard balls come close); inelastic collisions turn some kinetic energy into heat, sound and deformation. In a perfectly inelastic collision the objects stick together.
e is the ratio of separation speed to approach speed. e = 1 is perfectly elastic, e = 0 perfectly inelastic. A basketball on a hardwood floor is about 0.8; a car crash is closer to 0.1–0.2.
v = (m₁u₁ + m₂u₂) ÷ (m₁ + m₂). A 1,000 kg car at 20 m/s hitting a stationary 2,000 kg car and sticking moves off at 6.67 m/s.
The change in momentum in a crash is fixed by the speed; spreading it over a longer time reduces the average force. Doubling the stopping time halves the force on the occupant.
Yes, in every inelastic collision. Momentum is always conserved in a closed system, but kinetic energy can become heat, sound and deformation.
kg·m/s in SI, which is the same as newton-seconds (N·s). In imperial units, slug·ft/s or lb·ft/s are sometimes used.
Sources
Collision results assume a head-on, one-dimensional collision with no external forces during contact. Real crashes involve rotation, deformation and friction.