# Impulse and Momentum Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Mar 25, 2022

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 = mv

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

J = Δp = p₂ - p₁ = mv₂ - mv₁ = mΔv

Delta (Δ) is a symbol that means "change". For example, while p is the instantaneous momentum, Δp 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.

## Impulse equation

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

J = Ft

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.

## 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 impulse is connected to kinetic energy - make sure to read about it as well!

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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