Impulse Calculator

Enter the values you know and leave the unknown blank. Use force and time for J = F · Δt, or mass with both velocities for J = m · Δv. Fill in both sides and the calculator bridges between them.

Force (F)

Time interval (dt)

Mass (m)

Initial velocity (v1)

Final velocity (v2)

Impulse (J)

Show kinetic energy and work

Add the kinetic energy before and after, and the work done on the object.

Show the force vs impact-time chart

See how spreading the same impulse over a longer time lowers the peak force.

Please input values into the fields

Change in momentum: N⋅s

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Impulse is the effect of a force acting over time on an object. It measures how much that force has changed the motion of the object. This calculator provides two different ways to calculate impulse and shows their relationship. One method calculates impulse from the force and its duration, while the other method calculates it from mass and change in velocity.

What is Impulse?

Impulse is the product of a force and the time over which it acts. A small force acting for a long time can produce the same impulse as a large force acting for a short time. Because forces have direction, impulse is a vector. Its direction is the same as that of the resultant force. If the direction of the push is opposite to the direction of motion (defined as positive), then the impulse may be negative.

Since impulse causes a change in momentum, the units of impulse and momentum are the same. In SI units, it is measured in newton-seconds (N s), which is exactly equal to kilogram-meter per second (kg m/s).

Two formulas for impulse.

The first formula is a direct derivation of the definition and calculates the product of force and time.

J = F \cdot \Delta t

The second formula is derived from the impulse-momentum theorem which states that change in momentum equals the impulse. Since momentum is mass times velocity, then a change in momentum would be mass times a change in velocity.

J = \Delta p = m\,(v_2 - v_1)

If you set the two terms on the right side of the formula equal to each other, then you get the impulse-momentum equation. This is the central equation for this tool. If you enter known values for force, time, mass, initial velocity and final velocity, then the tool will calculate the remaining unknowns.

F \cdot \Delta t = m\,(v_2 - v_1)

Here's how to use this calculator:

Enter the known values and leave the unknown fields blank. In "Force-Time" mode, enter force and time to find impulse. In "Momentum" mode, enter mass and two velocities. You can also combine both modes. If you enter mass, two velocities, and time, the tool will first calculate the impulse from the change in velocity and then the force that produced that impulse. If you enter a value for impulse, the tool can calculate it. Conversely, you can also enter an impulse to find force, time, mass, and velocity.

Each field has a corresponding unit. Enter the values in Newtons or pounds for force, seconds or milliseconds for time and meters per second or kilometers per hour for speed. The results will be automatically converted.

Examples of calculations:

A baseball with a mass of 0.15 kg is hit by a bat. The bat exerts an average force of 1000 N for 0.01 seconds. We use the force-time formula.

J = F \cdot \Delta t = 1000 \times 0.01 = 10 \ \text{N s}

So the impulse produced by the bat is 10 Ns and the change in momentum of the ball is 10 kg m/s. If the ball was initially at rest, its final velocity will be equal to the ratio of the momentum to the mass which is approximately 67 meters per second. The same result can be obtained using the formula for impulse-momentum change. This is because both formulas are essentially expressing the same equation.

Symbol	Meaning	Example
J	Impulse (change in momentum)	10 N s
F	Average force	1000 N
dt	Time the force acts	0.01 s
m	Mass	0.15 kg
v1	Initial velocity	0 m/s
v2	Final velocity	about 67 m/s

Why impulse matters in real life.

The relationship between force and time of impact explains why many safety devices work. For a constant impulse, the force and contact time are inversely proportional. So any measure that increases the time of impact will reduce the maximum force exerted on you. Airbags and crush zones increase the time of impact. A boxer moves his body into the punch, a catcher pulls back to absorb momentum while catching a fast ball, and a lander bends its knees. All these methods spread out the same change in impulse over a longer period of time.

The same principle applies to the motion of objects as well. A rocket continually expels exhaust gases during combustion, thus building up impulse. The total impulse determines the change in momentum of the carrier. In sports, a longer follow-through results in the club or racket remaining in contact with the ball for a longer time, which increases the impulse and makes the ball go faster.

Impulse, momentum and work are not the same thing.

These three concepts are easily confused with each other. Momentum is a measure of the current motion of an object and is calculated by multiplying mass by velocity. The change in momentum is the change in that momentum, and it is determined by the product of force and time. Work is another effect produced by a force, and it is determined by the product of force and distance; it changes kinetic energy, not momentum. When you open up the energy options on a calculation tool, you will see initial and final kinetic energy next to momentum, which shows that the change in momentum is not equal to the change in kinetic energy.

Frequently asked questions

How do you calculate impulse?

You multiply the average force by its duration of action. That is, J = F*dt. If the force is unknown, you can use the change in momentum: J = m*(v2 − v1). In both cases, the unit of impulse is newton-second.

What is the impulse-momentum theorem?

It states that the impulse received by a body is equal to its change in momentum. The greater the impulse, the greater the change in momentum. Therefore, a longer duration of action or a larger force will result in a greater change in motion of the body.

Can the impulse be negative?

Yes, impulse is a vector. Negative values indicate that the direction of force and change in momentum are opposite to the chosen positive direction. An example would be when a ball bounces off a wall.

How does an air bag reduce impact forces?

Since the change in velocity determines momentum, it also determines impulse. The airbag lengthens the time required to stop the vehicle. Since force is equal to the change in momentum divided by the time, a longer time means less force on the body.

What is the unit of impulse?

The unit in the International System of Units (SI) is newton-second (N s), which is dimensionally equal to kilogram-metre per second (kg m/s). The latter is the unit of momentum, so impulse is a change in momentum.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

The Physics Classroom: Impulse-Momentum Change Theorem
Lesson on the link between impulse and momentum with worked examples.
HyperPhysics: Impulse of Force
Concise reference on impulse, force, and momentum change.