# Impulse and Momentum Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jan 19, 2023

This impulse and momentum calculator will help you analyze any object in motion. You will learn how to calculate impulse in three ways:

• knowing the change in velocity of a body,
• knowing the time a force acts on this body and
• simply from the change of momentum.

Keep reading to learn the impulse equation, and never worry about calculating momentum again!

## Formula for momentum

Momentum $p$ is a vector value defined as the product of the mass $m$ and velocity $v$ of an object:

$p = m \cdot v$

The change of a body's momentum is called impulse $J$:

\small\begin{align*} J &= \Delta p = p_2 - p_1 = m \cdot V_2 - m \cdot V_1\\ &=m \cdot \Delta V \end{align*}

Delta $(\Delta)$ is a symbol that means "change". For example, while $p$ is the instantaneous momentum, $\Delta p$ depicts the change of momentum that occurred over some period of time.

Head over to the conservation of momentum calculator to discover the practical applications of momentum. For calculating momentum in more than one dimension, head to our momentum calculator.

## Impulse equation

The impulse of a body is the product of time $t$ and force $F$ acting on that body:

$J = F \cdot t$

Units of both momentum and impulse are newton-seconds (symbol: N·s) expressed as kg·m/s in SI units.

Check if you can derive the above impulse equation from the formula J = mΔv. Hint: you will have to use the definition of acceleration and Newton's second law.

You will benefit from learning about specific impulse through our specific impulse calculator.

## How to calculate impulse

1. You can type the initial and final momentum values into our calculator to find the impulse directly from the impulse formula J = Δp.
2. You can also enter the values of mass and velocity change of an object to calculate the impulse from the equation J = mΔv.
3. If you know the force acting on the object, enter the values of force and time change instead. Our impulse and momentum calculator will use the J = Ft formula.

The concept of recoil energy and impulse are interrelated. Our recoil energy calculator will help you understand more.

## FAQ

### How do I calculate impulse from momentum?

You can calculate impulse from momentum by taking the difference in momentum between the initial (p1) and final (p2) states. For this, we use the following impulse formula:

J = Δp = p2 - p1

Where J represents the impulse and Δp is the change in momentum.

### What's the impulse-momentum theorem?

According to the impulse-momentum theorem, the impulse applied to a moving object equals its change in momentum. If the impulse is negative, this means we're exerting the force in the opposite direction of the movement. If it's positive, the force and initial velocity are in the same direction.

### Are impulse and momentum the same thing?

No, but these are related concepts. Impulse J refers to the amount of force applied to a moving object over an interval of time, whereas momentum p represents the quantity of motion of the moving object. The impulse-momentum theorem connects these two factors as J = Δp, where Δp represents the change in momentum.

### What impulse is required to stop a ball if m=160g and v=2.5m/s?

An impulse of -0.4 N⋅s. To get this value:

1. Apply the impulse-momentum formula:

J = Δp = m × (v2 - v1)

where:

• J - Impulse;
• Δp - Change in momentum; and
• v2 and v1 - Final and initial velocities.
2. Substitute in the values and perform the necessary calculations:

J = 160 g × (0 m/s - 2.5 m/s)
J = -0.4 N⋅s

This negative result indicates that the impulse has to be contrary to the ball's direction of motion in order to stop the ball.

Bogna Szyk
Velocity change (Δv)
ft/s
Initial velocity (v₁)
ft/s
Final velocity (v₂)
ft/s
Mass (m)
lb
Force (F)
N
Time interval
sec
Impulse and momentum
Impulse (J)
N·s
Initial momentum (p₁)
N·s
Final momentum (p₂)
N·s
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