Impulse and Momentum Calculator

Calculate impulse, momentum, force, and velocity relationships

Input any eight values to solve for the remaining one using impulse-momentum relationships.

Last updated: December 24, 2025

CreatorFrank Zhao

Impulse and Momentum Variables

Velocity change (Δv)

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m/s

Initial velocity (v₁)

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m/s

Final velocity (v₂)

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m/s

Mass (m)

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Force (F)

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Time interval

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sec

Impulse (J)

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N⋅s

Initial momentum (p₁)

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N⋅s

Final momentum (p₂)

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N⋅s

1Impulse from ForceJ = F × t

J = F \cdot t

2Impulse from VelocityJ = m × Δv

J = m \cdot \Delta v

3Momentump = m × v

p = m \cdot v

4Velocity ChangeΔv = v₂ - v₁

\Delta v = v_2 - v_1

5Impulse TheoremJ = p₂ - p₁

J = p_2 - p_1

6Force from ImpulseF = (m × Δv) / t

F = \frac{m \cdot \Delta v}{t}

7Time from Impulset = J / F

t = \frac{J}{F}

JImpulse

FForce

tTime

mMass

vVelocity

pMomentum

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Introduction / Overview

Impulse and momentum are two sides of the same story: momentum tells you how much “motion” an object has, and impulse tells you how much that motion changes. If you’re working on a physics homework problem, checking a lab measurement, or estimating the effect of a push, this calculator helps you connect the dots.

✅ One simple idea to remember: impulse is the change in momentum. In symbols: $J = \Delta p$ .

Who this is for

Students solving impulse-momentum problems quickly.
Teachers and tutors checking answers and sign conventions.
Engineers and hobbyists sanity-checking “push vs. time” estimates.

A good companion

If you only need basic momentum in one dimension, try our Momentum Calculator. For collisions and momentum conservation, the Conservation of Momentum Calculator is a natural next step.

🧱

Formula for momentum

Momentum is the mass–velocity product. In one dimension you can treat it as a signed number, but in general it’s a vector. The core definition is:

p = m \cdot v

Here $p$ is momentum, $m$ is mass, and $v$ is velocity.

Why signs matter

If you pick “to the right” as positive, then a leftward velocity is negative. That’s why an impulse that stops a moving object often comes out negative — it’s pointing opposite the motion.

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Impulse equation

Impulse can be defined two equivalent ways: as force applied over time, or as the change in momentum. When the average force is known over a time interval, the most direct formula is:

J = F \cdot t

In SI units, $J$ is measured in $\mathrm{N\cdot s}$ , which is the same as $\mathrm{kg\cdot m/s}$ .

The same impulse can also be computed from momentum change:

J = \Delta p

=

p_2 - p_1

=

m\cdot v_2 - m\cdot v_1

=

m\cdot (v_2 - v_1)

=

m\cdot \Delta v

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How to use / Quick start guide

The calculator is flexible: enter any set of values you actually know, and it fills the rest. A simple way to use it is to pick one “path” (force–time, mass–velocity change, or momentum change) and start there.

Choose what you know

For example: mass and velocity change, or force and time.

Enter values with units

Units are handled for you. Just pick the unit you want for each field.

Read the blue results

Calculated outputs are highlighted, so you can quickly see what the calculator derived.

Worked example: stopping a ball

A ball with mass $m = 0.160\ \mathrm{kg}$ moves at $v_1 = 2.5\ \mathrm{m/s}$ and comes to rest $v_2 = 0\ \mathrm{m/s}$ . The required impulse is:

J = m\,(v_2 - v_1)

=

0.160\,(0 - 2.5)

=

-0.4\ \mathrm{N\cdot s}

The negative sign simply means the impulse points opposite the initial motion.

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How to calculate impulse

1) From momentum change

If you know initial and final momentum, use $J = p_2 - p_1$ .

2) From mass and velocity change

If you know mass and velocity change, use $J = m\,\Delta v$ .

3) From force and time

If you know average force and time interval, use $J = F\,t$ .

💡

Tip:

If you don’t know the exact force profile (it changes over time), using an average force can still be a solid estimate — just treat the result as approximate.

🌍

Real-world examples / Use cases

⚽

Stopping a ball

Background: a ball is moving and you want the impulse needed to bring it to rest.

J = 0.160\,(0 - 2.5)

=

-0.4\ \mathrm{N\cdot s}

Use it to estimate the “push back” required, or to compare two stopping times for the same change in momentum.

🛹

Push over a short time

Background: a skateboard gets a push of roughly constant force.

J = F\,t

=

50\times 0.20

=

10\ \mathrm{N\cdot s}

If mass is $m = 2\ \mathrm{kg}$ , then $\Delta v = J/m = 5\ \mathrm{m/s}$ .

🧤

Catching safely

Background: the same impulse can be delivered with a smaller force if you increase the stopping time.

J = F\,t

\Rightarrow

F = J/t

Practical takeaway: “give” in gloves, padding, or bending your arms increases $t$ and reduces average $F$ .

🎯

Checking a collision setup

Background: you computed momenta before and after an interaction and want the impulse.

J = p_2 - p_1

For two-object problems, switch to the Conservation of Momentum Calculator.

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Tips & best practices

•Pick a positive direction first, then keep signs consistent for $v_1$ , $v_2$ , $p_1$ , and $p_2$ .
•If you’re using $J = F\,t$ , remember it assumes an average force over the interval.
•Use consistent units: SI makes life easy (kg, m/s, N, s). The calculator converts for you, but keeping inputs “reasonable” helps avoid mistakes.
•For the most accurate interpretation, focus on $J$ as a vector direction — not just a magnitude.

💡

Pro Tip: If your result looks wildly large or tiny, try switching the units to something closer to the scale you expect (for example, hours instead of seconds).

📐

Calculation method / Formula explanation

The calculator connects three core relationships. You can think of them as three “doors” into the same physics.

Momentum definition

p = m\,v

Impulse from force and time

J = F\,t

Impulse-momentum relationship

J = \Delta p = p_2 - p_1

\Delta v = v_2 - v_1

\Rightarrow

J = m\,\Delta v

Variable meanings

$m$ : mass
$v_1$ , $v_2$ : initial and final velocity
$p_1$ , $p_2$ : initial and final momentum
$F$ : average force during the interval
$t$ : time interval
$J$ : impulse

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Frequently asked questions (FAQs)

How do I calculate impulse from momentum?

Use the difference between final and initial momentum: $J = \Delta p = p_2 - p_1$ .

What’s the impulse–momentum theorem?

It states that the impulse applied to an object equals its change in momentum: $J = \Delta p$ . A negative value usually means the impulse points opposite the chosen positive direction.

Are impulse and momentum the same thing?

They’re related but not identical. Momentum measures motion at an instant: $p = m\,v$ . Impulse measures how much momentum changes over an interval: $J = \Delta p$ .

What impulse is required to stop a ball if mass is 160 g and speed is 2.5 m/s?

Convert mass to kilograms and set the final velocity to zero.

J = m\,(v_2 - v_1)

=

0.160\,(0 - 2.5)

=

-0.4\ \mathrm{N\cdot s}

The negative sign means the stopping impulse points opposite the ball’s motion.

Why do I get a negative impulse?

Impulse is directional. If you define one direction as positive, a result like $J < 0$ means the impulse is pointing in the opposite direction.

What units should impulse and momentum use?

In SI, both share the same unit: $\mathrm{N\cdot s}$ which is equivalent to $\mathrm{kg\cdot m/s}$ .

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Limitations / Disclaimers

•This calculator is for educational and estimation purposes. It does not replace professional engineering judgment.
•Using $J = F\,t$ assumes an average force over the time interval; real forces may vary significantly.
•All results depend on your sign convention and choice of direction for $v$ and $p$ .
•For multi-dimensional motion, you should treat momentum and impulse as vectors; this calculator focuses on one-dimensional relationships.

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