Angular Velocity Calculator

Use our angular velocity calculator to find velocity using one of two different methods.

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Angular Velocity Formula

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How to Calculate Angular Velocity

Angular velocity describes how fast an object rotates or revolves relative to another point. It’s a vector quantity, which means it has both a magnitude (how fast the object spins) and a direction (along the axis of rotation).

More specifically, angular velocity is a measure of the rate of change of the angular position of an object as it rotates about an axis. It tells us how quickly an object is rotating.

The standard unit of angular velocity is radians per second (rad/s), but it can also be expressed in degrees per second or revolutions per minute (rpm).

Angular Velocity Formulas

There are several formulas that you can use to find the angular velocity of an object.

Angular Velocity Using Radius and Linear Velocity

One way to calculate angular velocity is by using the radius of the circular path and the linear velocity= of the moving object. The formula to find angular velocity ω when the radius r and linear velocity v are known is:


Thus, the angular velocity of an object ω is equal to its linear velocity v divided by the radius of its path r.

Angular Velocity Using the Change in Angle Over Time

Another approach to calculate angular velocity is to consider the change in angle over time. If an object rotates through an angle Δα (measured in radians) in a time period t, the angular velocity can be calculated as:

\omega=\frac{\Delta \alpha}{t}

So, the angular velocity of an object ω is equal to the angle of change in its direction Δα divided by the time it takes for the change in angle to occur t.

For example, suppose a bicycle wheel has a radius of 0.3 meters. If the wheel is rolling such that the linear velocity of a point on the rim is 1.885 meters per second, what is the angular velocity of the wheel?

Let’s start by calculating this using the radius and linear velocity:

\omega=\frac{1.885\ m/s}{0.3\ m}=6.28\ rad/s

The angular velocity of the wheel is equal to 6.28 radians per second.

Suppose now that the same wheel makes a full rotation in 1 second. Recall that 1 full rotation is equal to 2π radians (you can double-check that using our revolutions to radians converter).

\omega=\frac{2\ \pi}{1\ s}=6.28\ rad/s

Using this method, observe that the angular velocity of the wheel is still equal to 6.28 radians per second.

Notice how both methods provide the same results, demonstrating the consistency and reliability of physics in describing the natural world.

You might also be interested in our angular acceleration calculator.