Frequency Calculator

What the frequency calculator does

Frequency is how many times a wave cycles each second. This calculator finds it from the wave's speed and its wavelength, and it works for any wave, with built-in speeds for light and sound in various materials. It also reports the period, the time for one cycle.

Below is what frequency is, the equation behind it, how it relates to the period, and a worked example.

How to use it

1. Pick a preset medium to fill in the wave speed, or enter your own wave velocity.
2. Enter the wavelength, with its unit.
3. Press Calculate for the frequency and the period, or Reset to clear them.

What frequency is

Frequency is the rate at which a wave repeats, the number of complete cycles that pass a fixed point each second. It is measured in hertz, where one hertz means one cycle per second. A wave that oscillates a thousand times a second has a frequency of a thousand hertz, and one that oscillates a billion times a second, a billion hertz. Frequency is, in a sense, how fast the wave is wiggling.

It is the property we most directly perceive in many waves. The frequency of a sound wave is its pitch, with high frequencies sounding high and low frequencies sounding low. The frequency of light sets its colour. The frequency of a radio wave is what you tune to on a dial. From music to broadcasting to the colours of the spectrum, frequency is the quantity that identifies a wave, and this calculator computes it from the wave's speed and length.

The equation it uses

Frequency is the wave's speed divided by its wavelength:

f = v ÷ λ

Here f is the frequency, v is the wave's speed, and λ is its wavelength. The reasoning mirrors that for wavelength: in one second the wave travels a distance equal to its speed, and the number of complete cycles in that distance is the speed divided by the length of one cycle. The calculator takes the speed from your chosen medium and divides by the wavelength you enter, then also works out the period from the result.

Frequency and period

The period is the close partner of frequency: it is the time taken for a single cycle to complete, while frequency is the number of cycles per unit time. The two are simply reciprocals of each other, so the period is one divided by the frequency, and the frequency is one divided by the period. A high frequency means a short period, since rapid cycles each take little time; a low frequency means a long period.

The calculator reports both because each is natural in different situations. Frequency is the usual way to describe sound, light, and radio, where you care how rapidly the wave oscillates. The period is often handier for slow, repeating events, like the swing of a pendulum or the turning of a wheel, where the time for one cycle is the obvious thing to measure. Having both lets you read the wave whichever way fits.

Frequency across the spectrum

Frequency spans an astonishing range across the waves around us. Audible sound runs from about 20 hertz at the lowest bass to around 20,000 hertz at the highest treble the human ear can catch. Radio waves climb into the millions and billions of hertz. Visible light oscillates at hundreds of trillions of hertz, far too fast to perceive as anything but colour, and beyond it, ultraviolet, X-rays, and gamma rays reach frequencies higher still.

What unites this enormous spread is the same simple relationship between speed, wavelength, and frequency. Whether the wave is a slow ocean swell or a gamma ray, dividing its speed by its wavelength gives its frequency. The calculator handles the whole range, which is why its frequency units run from hertz all the way up to terahertz, covering everything from a hum to the highest-frequency light.

Units and precision

The calculator works in SI units underneath, with speed in metres per second and wavelength in metres, and it reports the frequency from hertz up to terahertz, along with the period in units from seconds down to picoseconds. The medium presets carry the standard speeds of light and sound in various materials, and a custom speed can be entered for any other wave. Results carry several significant figures.

A worked example

Take green light with a wavelength of 555 nanometres, travelling at the speed of light in vacuum.

The frequency is f = v ÷ λ = 299,792,458 ÷ (555 × 10⁻⁹) ≈ 540 terahertz, which is 540 trillion cycles per second. The period, the time for a single oscillation, is the reciprocal of that, an almost unimaginably brief 1.9 femtoseconds. These dizzying numbers are why we never perceive light's flickering directly, only its colour.

Questions people ask

How do you calculate frequency?

Divide the wave's speed by its wavelength, f = v/λ. The result is the number of cycles per second, measured in hertz.

What is the relationship between frequency and period?

They are reciprocals. The period is one divided by the frequency, the time for one cycle, and the frequency is one divided by the period. High frequency means short period.

Is frequency the same as pitch?

For sound, yes, in effect. The frequency of a sound wave determines its pitch, with higher frequencies heard as higher notes and lower frequencies as lower ones.

What is a hertz?

The unit of frequency, equal to one cycle per second. A kilohertz is a thousand cycles per second, a megahertz a million, and a terahertz a trillion.

References

A quick note on where the physics comes from. The wave relationship linking speed, frequency, and wavelength, and the reciprocal tie between frequency and period, are standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The SI units follow the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 1, Section 16.1, Traveling Waves. https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves
2. HyperPhysics, Frequency, Period and Wave Relationship. http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/wavms.html
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811