Period Calculator

How it works

1. 1Choose your known quantity — frequency, angular velocity, or pendulum length — from the “Calculate from” dropdown.
2. 2Enter the value. For pendulum length you can switch between metres and feet using the Metric / Imperial toggle.
3. 3The calculator applies the matching formula (T = 1/f, T = 2π/ω, or T = 2π√(L/g)) and shows the period in seconds with the corresponding frequency.

Use cases

• Find the period of an AC supply or audio signal from its frequency (a 50 Hz mains supply has T = 0.02 s).
• Find how long one revolution takes for a rotating shaft or carousel from its angular velocity.
• Estimate the swing period of a grandfather clock or any simple pendulum from its length.

Frequently asked questions

What is the formula for period from frequency?

T = 1 ÷ f, where T is the period in seconds and f is the frequency in hertz. For example, a signal at f = 2 Hz completes one cycle every T = 1 ÷ 2 = 0.5 s.

How do I calculate period from angular velocity?

T = 2π ÷ ω, where ω is the angular velocity in rad/s. One revolution spans 2π radians, so dividing by ω gives the time per revolution. For ω = 2π rad/s, T = 1 s.

What is the pendulum period formula and how accurate is it?

T = 2π·√(L ÷ g), where L is the length in metres and g ≈ 9.80665 m/s². It is exact for small swing angles and within ~1% for swings up to about 15°. A 1 m pendulum gives T ≈ 2.0 s, so each half-swing takes about 1 s.