Frequency to Wavelength Calculator — λ = v/f

How it works

Every wave obeys one simple relation between its speed, frequency and wavelength:

v = f × λ

where v is the wave speed, f is the frequency (how many cycles pass per second, in hertz) and λ is the wavelength (the length of one cycle). Solving for the wavelength gives what this calculator returns:

λ = v ÷ f

The wave speed depends on the medium: sound travels at about 343 m/s in air, while light and other electromagnetic waves travel at about 3 × 10⁸ m/s in a vacuum. Enter the speed and frequency in consistent units — m/s and hertz give a wavelength in metres. Higher frequency means a shorter wavelength, and vice versa.

To go the other way, rearrange: the frequency is f = v ÷ λ, and the wave speed is v = f × λ.

Worked example

Concert A (440 Hz) as a sound wave in air (343 m/s) has a wavelength of 343 ÷ 440 = 0.78 m. Middle C (262 Hz) is lower, so its wavelength is longer: 343 ÷ 262 = 1.31 m. For an FM radio station at 100 MHz, the wave is electromagnetic and travels at 3 × 10⁸ m/s, giving 3 × 10⁸ ÷ 1 × 10⁸ = 3 m — which is why FM antennas are around a metre long.

Frequently asked questions

How do I convert frequency to wavelength?

Divide the wave speed by the frequency: λ = v ÷ f. You need the speed of the wave in its medium — about 343 m/s for sound in air, or 3 × 10⁸ m/s for light and radio in a vacuum.

What is the relationship between frequency and wavelength?

They are inversely proportional at a fixed wave speed: v = fλ. Double the frequency and the wavelength halves; halve the frequency and it doubles. Their product always equals the wave speed.

What wave speed should I use?

Use the speed of the wave in its medium. Sound in air is roughly 343 m/s (it varies with temperature); electromagnetic waves — light, radio, microwaves — travel at about 3 × 10⁸ m/s in a vacuum and slightly slower in air. Sound in water or solids is faster than in air.

How do I find frequency from wavelength instead?

Rearrange the same relation to f = v ÷ λ: divide the wave speed by the wavelength. For example, a 3 m radio wave travelling at 3 × 10⁸ m/s has a frequency of 3 × 10⁸ ÷ 3 = 1 × 10⁸ Hz, or 100 MHz.

What units does wavelength use?

Whatever your inputs imply. Wave speed in metres per second and frequency in hertz (cycles per second) give a wavelength in metres. This calculator treats the numbers as unit-agnostic, so keep the speed and frequency units consistent.

Does this work for both sound and light?

Yes — v = fλ holds for all waves. The only difference is the wave speed you enter: around 343 m/s for sound in air, or about 3 × 10⁸ m/s for light and other electromagnetic waves. Set the correct speed for your wave and the wavelength follows.