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Angular speed and frequency calculator

A-level Motion

Angular speed in radians per second from the frequency of rotation.

ω = 2πf

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

31.4 rad/s

Working

  1. Write the equation
    ω = 2πf
  2. Substitute the values
    ω = 2π × 5
  3. Calculate
    ω = 31.4159 rad/s
  4. Give the answer to 3 significant figures
    ω = 31.4 rad/s

Worked example

Find ω, the angular speed. Given: frequency f = 5.00 Hz.

  1. Write the equation
    ω = 2πf
  2. Substitute the values
    ω = 2π × 5
  3. Calculate
    ω = 31.4159 rad/s
  4. Give the answer to 3 significant figures
    ω = 31.4 rad/s

Symbols and units

SymbolQuantitySI unit
ωAngular speedrad/s
fFrequencyHz

Angular speed and frequency: rearranged

  • To find angular speed: ω = 2πf
  • To find frequency: f = ω / (2π)

Exam tip

One revolution is 2π radians. To use rev/min, choose that unit rather than converting by hand.

Common questions

What is the formula for angular speed and frequency?

The equation is ω = 2πf, where ω is the angular speed (rad/s); f is the frequency (Hz).

What units should I use for angular speed and frequency?

In SI units: angular speed in rad/s, frequency in Hz. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange ω = 2πf?

Rearranging gives these forms: to find angular speed: ω = 2πf. to find frequency: f = ω / (2π).

Practise angular speed and frequency questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

More motion equations: Speed, distance and time, Acceleration, Final velocity, Velocity squared, Displacement under constant acceleration, Displacement from average velocity, Momentum, Force and change in momentum. See the full list on the a-level physics equation calculator page.