Angular Velocity Calculator

What Is Angular Velocity?

Angular velocity describes how fast an object rotates or revolves. It measures the angle an object sweeps through per unit of time and is typically expressed in radians per second (rad/s), revolutions per minute (RPM), or degrees per second (°/s).

Angular velocity is a key concept in rotational mechanics, used to describe everything from motors and turbines to the rotation of the Earth. It is the rotational analog of the linear velocity you would calculate for an object moving in a straight line.

How to Calculate Angular Velocity

There are two common ways to calculate angular velocity, depending on what information you have available.

Angular Velocity from RPM

If you know an object's rotational speed in revolutions per minute, you can convert to radians per second using the following formula:

For example, a standard US electrical motor running at 1,800 RPM has an angular velocity of:

ω = 2π × 1,800 / 60 = 188.5 rad/s

Angular Velocity from Angle and Time

If you know the angle swept and the time taken, use:

Where θ is the angle in radians and t is the time in seconds.

Relationship to Linear Velocity

Linear speed at the rim of a rotating object is related to angular velocity by v = ω × r, where r is the radius. This is why larger wheels cover more ground per revolution. It is also the basis for calculating centripetal force and angular acceleration.