# Angular Momentum Calculator

Our angular momentum calculator is the perfect tool for **obtaining the angular momentum of a point object rotating around a fixed origin or finding the angular momentum of a rotating rigid body**.

Keep reading while we walk you through everything you need to know about angular momentum, including:

- What
**angular momentum**is; - How to find the angular momentum of a
**particle**or**rigid body**; - What is the
**unit for angular momentum**; and **More**!

## What is angular momentum?

The angular momentum is the linear momentum analog for rotations. It's a **vector quantity** describing the *rotational momentum* of an object.

Like linear momentum, it's a **conserved quantity**: given no external *torques*, it remains constant.

💡 Read more about this in our conservation of momentum calculator.

We can define two types of angular momentum:

- The angular momentum of a
**point particle relative to a fixed point in space**; and - The angular momentum of a
**rigid body around its center of rotation**.

Let's now look at how to calculate angular momentum.

## Angular momentum formula

As we said, we'll have two analogous formulas for angular momentum: for **point particles** and **rigid bodies**.

### Angular momentum of a point particle

For a **point particle rotating around a fixed point** (a satellite orbiting the Earth, for example), the angular momentum $\vec{L}$ is the **cross product** between the **position** vector $\vec{r}$ and the **linear momentum** of the particle $\vec{p}$:

and in terms of the particle's velocity $\vec{v}$:

Its orientation is given by the **right-hand rule**: *we wrap our right-hand fingers around the trajectory of the particle, and our thumb will point in the same direction as the resulting angular momentum*.

### Angular momentum of a rotating rigid body

For a **rotating rigid body**, such as the Earth, the angular momentum about an axis is the product between its **moment of inertia** $I$ and its **angular velocity** $\vec{\omega}$:

🙋 You can find the angular momentum for either case with our angular momentum calculator. Simply **select the formula at the top of the calculator and start experimenting with it!**

## What is the unit for angular momentum

The **SI, International System of Units** unit for angular momentum is the **kilogram meter squared per second (kg ⋅ m²/s)**.

With our angular momentum calculator, you can input the parameters using any unit, and **it will automatically convert the angular momentum to this SI unit**.