How do I convert frequency to wavelength?

Divide the wave speed by the frequency. For radio, use the speed of light: 100 MHz gives a 3 metre wavelength.

What speed should I use for sound?

About 343 m/s in air at 20°C. Using the speed of light for sound is the most common mistake and gives answers a million times too large.

Why are Wi-Fi antennas so small?

Antenna size scales with wavelength. At 2.4 GHz the wavelength is about 12.5 cm, so a quarter-wave antenna is roughly 3 cm.

Does frequency change in a different medium?

No, frequency stays constant. Wave speed and wavelength both change, which is why light refracts when entering glass or water.

Frequency & Wavelength Calculator - Convert Either Way

Frequency and Wavelength Calculator

Frequency and wavelength are inversely related through wave speed. Enter either one and this calculator returns the other.

Formula

λ = c ÷ f · f = c ÷ λ

c = 299,792,458 m/s in a vacuum
For sound use roughly 343 m/s in air at 20 °C instead

FM at 100 MHz: 299,792,458 ÷ 100,000,000 = 3.00 m

The Wave Equation

v = f × λ

Where v is wave speed, f frequency in hertz and λ wavelength in metres. Rearranged: λ = v ÷ f.

For electromagnetic waves in a vacuum, v is the speed of light: 299,792,458 m/s, usually rounded to 3 × 10⁸.

A 100 MHz FM radio station has a wavelength of 3 × 10⁸ ÷ 1 × 10⁸ = 3 metres.

Use the Right Wave Speed

The commonest error is using the speed of light for sound. Sound travels at roughly 343 m/s in air at 20°C — about a million times slower.

A 440 Hz concert A therefore has a wavelength of 343 ÷ 440 = 0.78 m, not hundreds of kilometres. Sound also travels faster in water (about 1,480 m/s) and faster still in steel.

Why Wavelength Determines Antenna Size

Antennas are sized in fractions of a wavelength, typically a quarter or a half. This is why an FM aerial is around 75 cm while a 2.4 GHz Wi-Fi antenna is only a few centimetres.

It also explains why long-wave radio reaches further around obstacles: longer wavelengths diffract more readily, while short microwave signals behave more like light and are blocked by walls.

Quick Reference

Wavelengths across the spectrum, which is why aerials differ so much in size.
Signal	Frequency	Wavelength
UK mains	50 Hz	5,996 km
Long wave radio	198 kHz	1,514 m
FM radio	100 MHz	3.00 m
Wi-Fi 2.4 GHz	2.4 GHz	12.5 cm
Wi-Fi 5 GHz	5 GHz	6.0 cm

Frequently Asked Questions

How do I convert frequency to wavelength?: Divide the wave speed by the frequency. For radio, use the speed of light: 100 MHz gives a 3 metre wavelength.
What speed should I use for sound?: About 343 m/s in air at 20°C. Using the speed of light for sound is the most common mistake and gives answers a million times too large.
Why are Wi-Fi antennas so small?: Antenna size scales with wavelength. At 2.4 GHz the wavelength is about 12.5 cm, so a quarter-wave antenna is roughly 3 cm.
Does frequency change in a different medium?: No, frequency stays constant. Wave speed and wavelength both change, which is why light refracts when entering glass or water.