Angular Velocity Calculator

Created by Dominik Czernia, PhD candidate
Last updated: Jun 30, 2022

With the angular velocity calculator, you can quickly work out the necessary parameters related to the angular speed. There are two methods to achieve that:

  1. Use the definition of the angular velocity, i.e., the angle change and time ratio. You can estimate the former using the angular displacement calculator.
  2. Use the linear velocity to angular velocity conversion. It bases on the angular speed formula with radius.
  3. Note that the angular velocity calculator has an advanced mode for the first method, which you can enter by clicking the button Advanced mode below the tool.

Read the following text to learn what angular velocity is, how to find angular speed, what angular velocity units are, and how to convert RPM to the angular velocity. You can see how to use this physical quantity in practice in the Omni's gear ratio calculator.

How to find angular speed

Let's start by explaining what angular velocity is. One of its definitions says that the angular velocity formula describes how fast an object rotates around a specific axis:

ω=Δαt\omega = \frac{\Delta \alpha}{t}

where:

  • ω\omega - The angular velocity;
  • Δα\Delta \alpha - The change in angular position, e.g., an angle of rotation; and
  • tt - Time needed for the angular position change.

🙋 The angular velocity units are usually radians per second rad/s\text{rad/s}, but you can also use revolutions per minute RPM\text{RPM} or hertzes Hz\text{Hz}. For example, to convert RPM to angular velocity in rad/s\text{rad/s}, you need to multiply it by approximately 0.104720.10472. You can use the unit converter directly from our angular velocity calculator for that purpose.

If you consider a circular motion, then you can use another angular velocity formula which is basically a conversion from linear velocity to angular velocity:

ω=vr\omega = \frac{v}{r}

where:

  • vv - Linear velocity; and
  • rr - Radius of the circular trajectory.

These two approaches should explain how to calculate angular speed in most cases. If you're currently considering the rotational motion, then you should also try our other tool, where we explain what is the equation for torque and how to find it.

The angular velocity calculator

Our angular velocity calculator uses both of the mentioned angular speed formulae. If you want to know how to find the final angular velocity with the tool, follow the below steps:

  1. Decide which angular speed equation you want to use: based on the angle change or from the linear velocity.
  2. Input any two values to find the missing one.
  3. In the first method, you can also turn on the Advanced mode to enter the initial and final angles manually.

That's it! Now, you can try different topics on our website. For example, check how to calculate porosity using our porosity and permeability calculator, which describes these two quantities in detail.

Dominik Czernia, PhD candidate
#1 Angle difference
Angle change (Δα)
deg
Time (t)
sec
Angular velocity (ω)
rad/s
#2 Linear velocity
Velocity (v)
m/s
Radius (r)
m
Angular velocity (ω)
rad/s
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