Frequency is how many cycles happen per second, measured in hertz. A frequency of 50 hertz means 50 cycles every second, the rate of New Zealand's mains electricity.

How are frequency and period related?

Frequency and period are reciprocals: frequency equals one divided by the period, and the period equals one divided by the frequency. A period of 0.02 seconds is a frequency of 50 hertz.

How do I find frequency from a wave?

For a wave, frequency equals the wave speed divided by the wavelength. So a wave travelling faster, or with a shorter wavelength, has a higher frequency.

Frequency Calculator

This frequency calculator finds frequency two ways: from the period of a repeating event, and from the speed and wavelength of a wave. Frequency is how many cycles occur each second, measured in hertz, and it describes everything that repeats, from the swing of a pendulum and the spin of an engine to sound, light and radio waves. The first tool uses the simple reciprocal relationship between frequency and period: frequency is one divided by the period, and the period is one divided by the frequency, so you can type into either box and get the other. A period of 0.02 seconds, for instance, is a frequency of 50 hertz, the rate at which New Zealand's mains electricity alternates. The second tool uses the wave equation, where frequency equals the wave speed divided by the wavelength, so a faster wave or a shorter wavelength means a higher frequency. Enter the wave speed, such as about 343 metres per second for sound in air or about 300 million metres per second for light, together with the wavelength, and it returns the frequency. These relationships are central to the physics of waves, music, electronics and communications. Type a value into either tool to see the frequency update as you go.

Frequency and period

Period (seconds)

or Frequency (Hz)

50 Hz / period 0.02 s

Frequency from a wave

Wave speed (m/s)

Wavelength (m)

439.7 Hz

How it works

For the first tool, frequency is one over the period and the period is one over the frequency, so changing one updates the other. For the second, frequency is the wave speed divided by the wavelength, straight from the wave equation that links speed, frequency and wavelength.

Worked example

A period of 0.02 seconds gives a frequency of 1 over 0.02, which is 50 hertz. A sound wave at 343 metres per second with a wavelength of 0.78 metres has a frequency of 343 over 0.78, about 440 hertz, the musical note A.

Related calculators

Wavelength Calculator: wavelength from speed and frequency.
Velocity Calculator: speed and distance.
Scientific Notation Calculator: large and small numbers.
Percentage Calculator: percentages.

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