Angular Frequency Calculator

Created by Mihir Ketkar
Reviewed by Dominik Czernia, PhD candidate and Jack Bowater
Last updated: May 05, 2022

The angular frequency calculator will help you determine the angular frequency (also known as angular velocity) of a system. In the article below, we describe how to calculate the angular frequency for simple harmonic motion and rotatory motion, and show various angular frequency equations.

What is angular frequency?

Angular frequency is a scalar physical quantity that measures how quickly an object rotates or oscillates with respect to time. It is usually denoted by the Greek letters Ω or ω. We measure it in radians per second, the SI unit, or rpm (revolutions per minute). It differs from frequency by a factor of 2π.

What is the angular frequency formula?

Depending on the situation, we may ask questions like "How to calculate the angular velocity of a wheel?" or "What is the angular frequency of a pendulum?". To answer both of these questions, you will need to use different approaches, which we describe below:

• How to calculate the angular frequency of a rotating object?

You can use the basic angular frequency equation for rotating objects:

ω = Δθ / Δt

where:

• Δθ- Amount of rotation, expressed in radians; and
• Δt - Time, taken in seconds.

For example, if a tire turns 200 radians in 40 seconds, how do you calculate angular velocity of the wheel?

Solution: ω = 200 radians / 40 seconds which would mean that ω = 5 rad/s

In this case we should use the angular frequency equation for oscillating objects, which is :

ω = 2 * π * f = 2 * π / T

where:

• f - Frequency;
• T - Time period; and
• π - Pi, a mathematical constant approximately equal to 3.142 and is defined as the ratio between the circumference and the diameter of a circle. (It's quite the celebrity in the field of mathematics 😎).

For example, if a pendulum oscillates with a frequency of 2 Hz, how do you find the angular frequency in this case?

Solution: ω = 2 * 3.142 * 2 rad/s
which would mean that  ω = 12.566 rad/s

How to use the angular frequency calculator?

Now that we have answers to "What is angular frequency?" and "How to calculate angular velocity?", all that is left to learn is how to use the angular frequency calculator. Follow these simple instructions, and you'll be calculating in no time!

1. Understand which formula is correct.

Is the object spinning like a wheel? Or is it moving to-and-fro like a swing set? Both these kinds of motion have an angular frequency, but we calculate them differently. Depending on the situation, decide which angular frequency formula to use. For spinning or rotating objects, use the part labeled For rotating objects, and for oscillations, use the second section called For oscillating objects.

2. Note down values of the known variables.

Take a look at the information you have and that which you don't have. The equation for how to calculate angular velocity is linear, so rearranging the formula should be simple.

3. Make sure you use the right units.

One of the most common mistakes made by students (and teachers 😜) is to forget to use the appropriate units. Always check the units of variables. Use the dropdown menu at the end of the input box to change units.

Angular frequency can be expressed in terms of rad/s, rpm, cps, or Hz. Use our cps calculator to learn how to convert between them.

4. Enter the values.

Enter the values in the boxes, and voila! You'll have your answer in the box labeled Angular frequency. Pretty neat, right?

5. Use the calculator in reverse

Do you already have angular frequency and want to calculate some other variable? This calculator can do that too! Just enter the value in the box labeled Angular frequency to calculate other variables.

If you loved this calculator, be sure to check out our angular acceleration calculator!

Mihir Ketkar
For rotating objects
Angular displacement
Time taken
sec
Angular frequency
For oscillating objects
Time period
sec
Frequency
Hz
Angular frequency
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