Circular motion tool

Rotational Frequency Calculator

Solve rotational frequency, rotation period, or angular velocity using f = ω / 2π.

Enter one known value

Solve a rotational frequency problem

Free tool
rad/s

Enter a positive finite value.

Use hertz for rotational frequency, radians per second for angular velocity, and seconds for rotation period.

Try an example:

Your rotational frequency result will appear here

Choose the required value and enter one known measurement.

Physics overview

What is rotational frequency?

Rotational frequency is the number of complete rotations or cycles an object completes each second.

Formula

Rotational frequency formula

Rotational Frequencyf = ω / 2π

  • f is rotational frequency in hertz.
  • T is rotation period in seconds.
  • ω is angular velocity in rad/s.

Worked example

A rotating object has an angular velocity of 12.566 rad/s

  1. Write the formula: f = ω / 2π.
  2. Substitute the value: f = 12.566 ÷ 2π.
  3. Calculate rotational frequency: f ≈ 2 Hz.

Rearranged equations

Solve for rotation period or angular velocity

Rotation period

T = 1 ÷ f

Divide one by rotational frequency.

Angular velocity

ω = 2πf

Multiply rotational frequency by 2π.

Physical relationship

Frequency, period, and angular velocity

Rotational frequency increases when angular velocity increases. Rotation period decreases as rotational frequency increases.

Units

Standard SI units

Use hertz for rotational frequency, seconds for rotation period, and radians per second for angular velocity.

Real-world applications

Where rotational frequency is used

  • Wheels, gears, and rotating disks.
  • Turbines and mechanical shafts.
  • Amusement rides and rotating platforms.
  • Planetary and satellite motion.
  • Motors and industrial machinery.

Calculation limits

Important assumptions

  • All entered values must be greater than zero.
  • Rotation period is the time required for one complete revolution.
  • Angular velocity must be entered in radians per second.
  • Direction is not represented.
  • Units are not converted automatically.

Related tools

Use the Angular Velocity Calculator to calculate angular velocity, displacement, or time.

Use the Centripetal Acceleration Calculator to calculate inward acceleration in circular motion.

Questions and answers

Rotational frequency calculator FAQ

What formula does the rotational frequency calculator use?

It uses f = ω / 2π, where rotational frequency equals angular velocity divided by 2π.

What is rotational frequency?

Rotational frequency is the number of complete rotations or cycles completed per second.

How do you calculate rotation period from rotational frequency?

Use T = 1 / f, where rotation period equals one divided by rotational frequency.

What units are used for rotational frequency?

Rotational frequency is measured in hertz, rotation period in seconds, and angular velocity in radians per second.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the Science Lab Tools Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Learn more about our formula-review and correction process, or read about Science Lab Tools.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently