Frequency and Wavelength Calculator

1. Enter any two of wave speed, frequency and wavelength.
2. Leave the one you want to find blank.
3. For light use a speed of about 3e8; for sound in air use about 343.
4. Read the result and the formula used.

Here is what each result means:

Every wave has a frequency, a wavelength and a speed, and they are tied together by one simple rule: the speed equals the frequency times the wavelength. Frequency is how many cycles pass a point each second, measured in hertz. Wavelength is the distance between one crest and the next, measured in meters. Multiply them and you get how fast the wave travels.

For a given speed, frequency and wavelength trade off against each other. A higher frequency means the wave cycles faster, so each wave is shorter and the wavelength drops. A lower frequency stretches the wave out into a longer wavelength. This is why a high-pitched sound has a short wavelength and a deep bass note a long one, even though both travel at the same speed through air.

The speed depends on the wave and the medium. Light and other electromagnetic waves travel at about 300 million meters per second in a vacuum, while sound in air moves at roughly 343 meters per second. Once you fix the speed for your wave, this calculator turns any frequency into its wavelength, or the other way round.

It rearranges one relation to solve for whichever value you leave blank.

1. For speed, multiply frequency by wavelength.
2. For frequency, divide speed by wavelength.
3. For wavelength, divide speed by frequency.

Waves carry energy and motion; see the velocity calculator and scientific notation calculator for large values like the speed of light.

A wave travels at 340 meters per second with a wavelength of 2 meters.

Calculation: f = v / wavelength = 340 / 2 = 170 hertz. To find the wavelength of a 440 hertz note in air, divide the speed of sound: 343 over 440 is about 0.78 meters.

One relation, rearranged for whatever you need to find.

All three come from speed equals frequency times wavelength, so any two of the values give the third. This single relation works for sound, light, water ripples and radio waves alike, as long as you use the correct wave speed for the medium.

The speed to use depends on the kind of wave and what it travels through.

Radio, microwaves, visible light and X-rays all travel at the speed of light, so their wavelengths follow directly from their frequencies. Sound travels far more slowly and speeds up in denser media, which is why the same note has a different wavelength in air and in water.

The Frequency

At a fixed speed, a higher frequency gives a shorter wavelength. The two are inversely related.

The Wave Speed

A faster wave at the same frequency has a longer wavelength. Speed depends on the medium.

The Medium

Moving a wave into a new medium changes its speed, which changes its wavelength while the frequency stays the same.

Physics Homework

Convert between frequency and wavelength for sound, light or radio waves.

Radio and Audio

Find the wavelength of a broadcast frequency or the pitch of a musical note.

Optics and Science

Relate the colour of light to its frequency using the speed of light.

1. Wrong Wave Speed

Use the speed of light for electromagnetic waves and the speed of sound for audio. They differ by a factor of nearly a million.

2. Mixing Units

Use hertz and meters, or convert kilohertz and centimeters first, for a speed in meters per second.

3. Confusing Frequency and Wavelength

Frequency is cycles per second; wavelength is a distance. They move in opposite directions.

4. Forgetting the Medium

Frequency stays the same across media, but speed and wavelength change.

5. Zero in a Divisor

Solving for frequency or wavelength cannot divide by zero.

The relation is exact; only the displayed decimals are rounded.

They are linked by the wave speed: speed equals frequency times wavelength. At a fixed speed a higher frequency means a shorter wavelength, and a lower frequency a longer one.

Divide the wave speed by the wavelength. A wave at 340 meters per second with a 2 meter wavelength has a frequency of 340 divided by 2, which is 170 hertz.

Divide the wave speed by the frequency. Leave the wavelength field blank and enter speed and frequency, and the calculator solves for it.

Use about 300,000,000 meters per second for light and other electromagnetic waves, and about 343 for sound in air. The speed depends on the wave and the medium.

Yes, at a fixed wave speed. Doubling the frequency halves the wavelength, because their product must stay equal to the speed.

The speed changes, so the wavelength changes too, but the frequency stays the same. This is why light bends when it passes into glass or water.

Meters per second for speed, hertz for frequency and meters for wavelength. Convert kilohertz, megahertz or centimeters to base units first.

Yes. The same rule applies to any wave. Just enter the correct speed: the speed of light for electromagnetic waves or the speed of sound for audio.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Wavelength (Wikipedia).
• Frequency (Wikipedia).
• Waves (Maths Is Fun).