Momentum Calculator
Put a 145 g ball moving at 40 m/s into the momentum calculator. The table shows the average force it takes to stop it in anything from a millisecond to a second.
Momentum
- Momentum p = mv = 0.145 kg × 40 m/s = 5.8 kg·m/s.
- 5.8 kg·m/s
- The unit algebra A newton is kg·m/s², so a newton-second is kg·m/s. That is why momentum and impulse (force × time) share a unit: a force acting for a time changes momentum by exactly F·Δt.
- kg·m/s = N·s
- In US units Equivalently 1.304 lbf·s.
- 41.95 lb·ft/s
- Kinetic energy at this speed ½mv², or p² / 2m. Momentum is conserved in every collision; kinetic energy only in perfectly elastic ones.
- 0.116 kJ (116 J)
- Speed used
- 40 m/s 144 km/h 89.48 mph 131.2 ft/s
| Stopping time | Average force | In lbf |
|---|---|---|
| 0.001 s | 5,800 N | 1,304 lbf |
| 0.01 s | 580 N | 130.4 lbf |
| 0.05 s | 116 N | 26.08 lbf |
| 0.1 s | 58 N | 13.04 lbf |
| 0.5 s | 11.6 N | 2.608 lbf |
| 1 s | 5.8 N | 1.304 lbf |
- Momentum is a vector: its sign follows the velocity. In a collision the total momentum of everything involved is the same before and after, whatever happens to the kinetic energy.
- Results are shown to four significant figures. Round to the precision of your least precise measurement.
How the Force Calculator works
p = mv. Momentum is mass times velocity. Kilograms and meters per second give kg·m/s, which is the same unit as a newton-second.
Worked example, the one above: a 145 g ball at 40 m/s. Convert the mass first: 0.145 kg. Then p = 0.145 × 40 = 5.8 kg·m/s. Its kinetic energy is ½ × 0.145 × 40² = 116 J.
Impulse: why stopping time matters. Newton's second law in its original form says force is the rate of change of momentum, F = Δp / Δt. To stop the ball, its 5.8 kg·m/s has to go to zero, and the average force needed is 5.8 divided by however long the stop takes. Stopped in a millisecond by a hard wall, that is 5,800 N. Stopped over 50 milliseconds by a glove that gives, it is 116 N. The momentum change is the same; spreading it over more time is what makes it survivable. Airbags, crumple zones, bent knees on landing and padded gloves all work by stretching Δt. The table under the result shows the force for a range of stopping times.
Momentum is conserved. In any collision or explosion with no outside force, the total momentum of everything involved is the same afterward as before. That is the third law in another form: the forces two bodies exert on each other are equal and opposite and act for the same time, so the momentum one gains the other loses. It is how a rifle recoils, how a rocket accelerates with nothing to push against, and how collision investigators work back to speeds.
Momentum has a direction. It is a vector, so velocity's sign carries through: a ball at −40 m/s has −5.8 kg·m/s. When two objects collide head on, their momenta partly cancel. Kinetic energy, by contrast, has no direction and does not cancel.
Momentum versus kinetic energy. They answer different questions. Momentum, linear in speed, says how hard something is to stop in a given time. Kinetic energy, ½mv², says how much damage stopping it does: how far it will dent or crush. A light fast object and a heavy slow one can have equal momentum and very different energies. And while momentum is always conserved in a collision, kinetic energy is conserved only if the collision is perfectly elastic.
The formula here is classical. At a significant fraction of the speed of light momentum becomes γmv and grows without limit as speed approaches c.
Force Calculator FAQ
What is the formula for momentum?
p = mv, mass times velocity. A 0.145 kg ball at 40 m/s has a momentum of 5.8 kg·m/s. The unit kg·m/s is the same as a newton-second.
What is the difference between momentum and impulse?
Impulse is force times the time it acts, F·Δt, and it equals the change in momentum it produces. They share a unit, N·s = kg·m/s. Stopping a 5.8 kg·m/s ball takes 5.8 N·s of impulse, delivered as a large force briefly or a small force for longer.
Is momentum always conserved?
The total momentum of a system is conserved whenever no net external force acts on it, which is true during almost any collision. Kinetic energy, by contrast, is conserved only in perfectly elastic collisions.
More from the Force Calculator
Sources
- NASA NSSDCA Moon Fact Sheet, bulk parameters table, row "Surface gravity (m/s2)", Moon column (page last updated January 11, 2024) (2026)
- NASA NSSDCA Mars Fact Sheet, bulk parameters table, row "Surface gravity (mean) (m/s2)", Mars column (page last updated May 19, 2025) (2026)