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

# Impulse and Momentum Calculator

By Bogna Haponiuk

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 Haponiuk