Impulse and Momentum Calculator

Solve force, time, velocity, and impulse with the impulse-momentum theorem.

Impulse-momentum calculation

Choose the unknown quantity, then enter the known motion and force values.

Calculation type

Mass (kg)

Initial velocity (m/s)

Average force (N)

Time duration (s)

About impulse and momentum

Linear momentum describes motion as the product of mass and velocity. A heavy object moving slowly can have the same momentum as a lighter object moving quickly. Because velocity includes direction, momentum is signed in a one-dimensional calculation. Choosing a positive direction before entering values is essential: motion or force in the opposite direction should be negative. Momentum is measured in kilogram metres per second. Impulse measures the effect of a force acting over a time interval. For a constant or average force, impulse equals force multiplied by duration. The impulse-momentum theorem states that this impulse equals the change in momentum. For an object whose mass remains constant, force times time equals mass times final velocity minus mass times initial velocity. This calculator rearranges that single relationship to solve final velocity, average force, time duration, or impulse. The theorem explains why extending stopping time can reduce average force. Airbags, padding, helmets, and follow-through in sports increase the time over which momentum changes. The total impulse needed to produce a given velocity change remains the same, but a longer duration means a smaller average force. Conversely, a very short collision can generate a large force even when the momentum change is moderate. Negative force or impulse indicates that the action points opposite the selected positive direction; it does not mean the calculation is invalid. This model assumes constant mass and uses an average net force. If force varies over time, the exact impulse is the area under the force-time curve rather than simply one instantaneous force multiplied by the whole interval. External forces should be combined into a net force, and multi-object collisions may require conservation of total system momentum in addition to this equation. Rockets and other variable-mass systems need a different treatment. Use the calculator for mechanics exercises, collision estimates, sports analysis, and quick engineering checks. Keep all values in SI units and use a consistent sign convention. For safety-critical impact analysis, measured force histories, structural deformation, and material response should supplement the ideal calculation.

Impulse and momentum examples

Each example rearranges the same impulse-momentum relationship.

Known values	Solved value	Scenario
0.145 kg, 40 m/s, 6500 N for 0.0015 s	Final velocity = 107.241379 m/s	Baseball hit
1500 kg, 15 to 0 m/s in 0.15 s	Average force = -150,000 N	Car stopping
500 kg, 100 to 150 m/s at 25,000 N	Time = 1 s	Engine burn
0.5 kg, -8 to 6 m/s	Impulse = 7 N·s	Bouncing ball

How to calculate impulse or momentum change

Choose the quantity you want to find.
Select a positive direction and enter velocities with the correct signs.
Enter the object's mass and the required force or time values.
Select Calculate and interpret the result using its sign and SI unit.

Frequently asked questions

What is the difference between impulse and momentum?

Momentum describes an object's current motion, while impulse describes a force acting over time. Impulse equals the change between final and initial momentum.

Why can force or impulse be negative?

A negative sign shows direction relative to the positive axis you selected. A braking force is commonly negative when forward motion is defined as positive.

Are N·s and kg·m/s equivalent?

Yes. A newton second reduces to kilogram metre per second, so both units can express impulse or momentum change.

Does a longer collision always reduce force?

For the same momentum change, increasing the stopping time reduces average force. The actual peak force still depends on the shape of the force-time curve.

Can this calculator model two colliding objects?

It solves the change for one constant-mass object. A two-object problem may first require conservation of total momentum to determine each final velocity.