Momentum Calculator
Momentum from mass and velocity, p = mv, or the mass or velocity from a momentum, plus impulse, FΔt, and the average force behind a change in velocity.
Result
Momentum: 132,000 lb·ft/s
Motion along one line; a minus sign means the opposite direction.
- Mass
- 3,000 lb
- Velocity
- 30 mph (44 ft/s)
- Kinetic energy
- 90,259 ft·lbf (122,375 J)
https://calcgallery.com/physics/momentum-calculator/
Results come from the published equations applied to the values you enter. They are not electrical design, conductor sizing, laboratory safety or medical guidance. Weather indices describe a standard person in standard conditions and are not a forecast. Where codes apply, local rules vary and must be checked. Read the full disclaimer
How to use the Momentum Calculator
- Choose what to find, the momentum, a mass or velocity from a momentum, an impulse, or the average force that changes a velocity.
- Enter the values, with a minus sign on any velocity or force that points the other way.
- Read the result in kilogram metres per second, or pound-feet per second in US units, with the kinetic energy or force that goes with it.
The formulas
p = m × vm = p ÷ v, v = p ÷ mimpulse J = F × Δt = Δpaverage force F = m × (v₂ − v₁) ÷ Δtkinetic energy K = ½ m v² = p² ÷ 2mMomentum and impulse share a unit: one newton second is one kilogram metre per second.
Limits
Everything is along one line, with direction as a sign. The force from a change in velocity is the average over the time; the peak force in an impact is higher, often much higher. Speeds approaching that of light need relativistic momentum instead.
With your numbers
- p = m × v = 3,000 lb × 44 ft/s = 132,000 lb·ft/s
Quick reference
Motion along one line; a minus sign means the opposite direction.
| Example | Result |
|---|---|
| 3,000 lb car at 30 mph | Momentum: 132,000 lb·ft/s |
| 1,400 kg car at 15 m/s | Momentum: 21,000 kg·m/s |
| Velocity of 1,400 kg with 21,000 kg·m/s | Velocity: 15 m/s |
| 50 N for 0.2 s | Impulse, the change in momentum: 10 kg·m/s |
| Stopping 87.8 kg from 27 m/s in 2.5 s | Average force: -947.8 N |
| The same in 0.2 s | Average force: -11,847 N |
| Ball, 0.145 kg, 40 m/s back at 50 m/s in 1 ms | Average force: -13,050 N |
Common questions about the Momentum Calculator
- How do I calculate momentum?
- Multiply the mass by the velocity: p = mv. A 1,400 kg car at 15 m/s has 21,000 kg·m/s, the example in OpenStax University Physics section 9.1. Momentum has a direction, so a car going the other way has −21,000 kg·m/s.
- What is impulse?
- The push a force gives over a time: J = FΔt, the average force times how long it acts. It equals the change in momentum it causes, which is the impulse–momentum theorem. 50 N for 0.2 s is an impulse of 10 N·s, which is the same unit as 10 kg·m/s.
- Why do airbags reduce the force of a crash?
- Stopping the person takes the same change in momentum however it happens, so spreading it over a longer time means a smaller average force. OpenStax example 9.2 stops an 860 N driver, about 87.8 kg, from 27 m/s: over 2.5 s the average force is about 948 N, but over 0.2 s it is about 11,850 N.
- How do I find the average force of an impact?
- Divide the change in momentum by the time it took: F = m(v₂ − v₁) ÷ Δt. A 0.145 kg ball arriving at 40 m/s and leaving at 50 m/s the other way, in a millisecond, changes velocity by −90 m/s; the average force is about 13,000 N, pointing back the way it came.
- How is momentum different from kinetic energy?
- Momentum, mv, has a direction and is conserved in every collision. Kinetic energy, ½mv², has none and is lost to heat and deformation in most real collisions. Double the speed and the momentum doubles while the kinetic energy quadruples; the page shows both.