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!

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.

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.

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 $\vec{\omega}$:

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.