Created By : Naaz Fatima

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 10, 2023

Angular Velocity is a free tool that displays the angular velocity in a fraction of seconds. All you need to do is enter the relevant inputs and our calculator gives answers to your questions immediately.

Angular Velocity Calculator: Have you ever worried about the calculation of Angular Velocity? Don't Panic as you can take help of our handy tool Angular Velocity Calculator and get the results in no time. Learn what is meant by angular velocity, formulas to calculate angular velocity, its units and relation between angular velocity and angular frequency, etc.

Choose a Calculation
Angle change (Δα):
Time (t):

Choose a Calculation
Velocity (v):
Radius (r):

What is meant by Angular Velocity?

Angular Velocity determines the rotational movement of objects and determines how fast they move around center of rotation. The faster the movement the greater is the Angular Velocity.

Angular Velocity Formula

In our calculator we use two different formulas to determine the Angular Velocity based on the inputs allotted. Angular Velocity Equation is similar to the equation of linear velocity. ω = (α₂ - α₁) / t = Δα / t

α₁ and α₂ are two angles on a circle and Δα is the difference. t is the time for which angle change occurs. In case of a normal velocity there is a positional change in the period. However, we will use an angle here instead of distance.

Angular Velocity 1

The other formula for angular velocity can be derived depending on the relation of linear velocity and radius using cross product i.e. v = ω × r

Angular Velocity 2

Rewriting this equation we can get the angular velocity as ω = r × v / |r|²

All other variables are vectors other than |r| and it is the absolute value of radius. Angular Velocity is a pseudovector and its direction is perpendicular to the plane of rotational movement.

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Angular Velocity Units

There are several units for Angular Velocity and some of them are listed as follows

  • Radians Per Second(rad/sec) - It tells how big the rotation is that the body moves in a given time.
  • Revolutions Per Minute(RPM) - It is mostly found unit in real time applications. It tells how fast a unit or wheel is spinning.
  • Hertz(Hz) - It is less frequently used for angular velocity and is a unit for frequency.

All of these units can be changed from one another using the relation. i.e. 1 RMP = 0.10472 rad/s = 0.01667 Hz

Difference between Angular Velocity and Angular Frequency

The formula for Angular Frequency is given by ω = 2 * π * f in which f is the frequency. It is evident that it also uses same letter and units are also same as rad/sec. There is a basic difference between angular velocity and angular frequency though both sound similar. Angular Frequency is a scalar is used in case of harmonic motion and Angular Velocity is a vector and is used for motion around a certain point.

FAQs on Angular Velocity Calculator

1. What is meant by Angular Velocity??

Angular Velocity is nothing but the velocity of a rotating object at a certain point in a given period of time.

2. What is the formula for Angular Velocity?

The Formula for Angular Velocity is given by ω = (α₂ - α₁) / t = Δα / t

3. What are the Units for Angular Velocity?

There are Several Units for Angular Velocity i.e. RPM or Radian Per Sec or Hertz.

4. Is Angular Velocity a Scalar or Vector?

Angular Velocity is a vector quantity since it has both direction and magnitude.