Momentum & Impulse Calculator

Understanding the momentum and impulse calculator — concept and principle

Momentum is the "quantity of motion" an object carries, the product of its mass and velocity. Impulse is what it takes to change that momentum: a force applied over a time. This calculator gives the momentum, the average force needed to stop the object in a chosen time, and its kinetic energy. It is used for collisions in sport, crash and drop safety, and physics problems.

Same momentum to remove: stop it faster and the force is larger.

How it is calculated

Momentum: p = m v, in kg·m/s, with m in kg and v in m/s.
Average stopping force: F = m v ÷ Δt, from the impulse–momentum theorem J = F Δt = Δp, with Δt in seconds.
Kinetic energy: KE = ½ m v², in joules.

The principle

Newton's second law in its original form says force equals the rate of change of momentum, F = Δp ÷ Δt. Rearranged, the impulse F Δt equals the change in momentum. A given momentum can be removed by a large force over a short time or a small force over a long time. That is the whole idea behind airbags, crumple zones, gym mats and bending your knees when you land: they lengthen Δt and so lower the average force. Kinetic energy, by contrast, depends on v², and must be absorbed over a stopping distance rather than a time.

Worked example

Inputs: m = 0.145 kg (a baseball), v = 40 m/s, Δt = 0.001 s.
Momentum: 0.145 × 40 = 5.8 kg·m/s.
Average force to stop: 5.8 ÷ 0.001 = 5,800 N.
Kinetic energy: ½ × 0.145 × 40² = 116 J.

Each point is the calculator re-run with only “Mass (kg)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Mass (kg)	Momentum (kg·m/s)
0.0362	1.45
0.0725	2.9
0.109	4.35
0.145	5.8
0.181	7.25
0.217	8.7
0.29	11.6

How to read the result

5,800 N is about 590 kgf, a huge force but acting for only a millisecond. Doubling the contact time halves the average force; peak forces during an impact are higher than the average. The calculator assumes the object comes to rest. If it bounces back or a bat sends it the other way, the momentum change is larger, up to about twice as much for a reversal at similar speed, and so is the force.

Common mistakes

Entering time in milliseconds instead of seconds.
Ignoring direction: momentum is a vector, and a rebound changes it by more than mv.
Confusing momentum (proportional to v) with kinetic energy (proportional to v²).

Keep in mind: The result is an average force over an idealised constant-duration impact. It is not suitable for protective-equipment or structural design, which require testing and qualified engineering.

Frequently asked questions

What is the difference between impulse and momentum?

Momentum is a property of a moving object; impulse is the change in momentum caused by a force acting over time. Both have the same unit, N·s = kg·m/s.

Why do airbags reduce injury?

They extend the stopping time and spread the force over a larger area, lowering both average force and pressure on the body.

Is momentum conserved in a collision?

Yes, the total momentum of an isolated system is conserved in every collision, even when kinetic energy is lost.

Sources: Isaac Newton, Philosophiæ Naturalis Principia Mathematica, 1687 · Halliday, Resnick and Walker, Fundamentals of Physics, Wiley · Robert K. Adair, The Physics of Baseball, Harper Perennial

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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