Wavelength Calculator

Wavelength is the distance between two identical points on a wave, such as one crest to the next. It's denoted by the Greek letter lambda (λ) and is a length measurement: Radio frequencies are usually given in meters, while light is often measured in nanometers.

This calculator will calculate the wavelength in four different ways based on the information you input. You can either input the frequency, speed of propagation and frequency, energy of a photon or the wavelength itself; then the calculator will give back the wavelength as well as the corresponding frequency and the energy of the photon.

The wave equation.

Any propagating wave follows a simple relationship: The speed is equal to the frequency times the wavelength.

To rearrange to find wavelength, the equation is: wavelength equals speed divided by frequency. The speed refers to how fast the wave moves, while the frequency refers to the number of cycles per second (measured in hertz). The calculated wavelength will be a length measurement.

Since the wavelength is equal to speed divided by frequency, it follows that at constant speed the shorter the wavelength, the higher the frequency. The two quantities are in an inverse relationship: doubling the frequency halves the wavelength.

The four modes of this computer:

Select the option that matches your question from above and the interface will only show the input fields required for that option. Each mode uses different inputs but is based on the same physics.

1. Calculation based on the frequency of light or other electromagnetic waves:

Light, radio waves, microwaves and X-rays are all electromagnetic waves. In a vacuum they all travel at the same speed - the speed of light (c), which is 299,792,458 metres per second. So the wavelength equals c divided by the frequency.

A radio station with a frequency of 100 MHz broadcasts radio waves with a wavelength of about 3 meters. A Wi-Fi signal with a frequency of 2.4 GHz has a wavelength of about 12.5 centimeters. Green light with a frequency near 550 THz has a wavelength of about 545 nanometers.

In glass or water the light slows down, which shortens its wavelength. The index of refraction n tells how much the speed changes: the speed in the medium is c divided by n, and the wavelength becomes c divided by n divided by f. The index of refraction for water is about 1.33, while it's about 1.5 for glass. The frequency doesn't change, so neither does color or photon energy; only the wavelength changes.

2. Calculate any wave based on speed of sound and frequency

Sound waves, surface waves and vibrations are not electromagnetic waves and have a much lower propagation speed than light. So you need to enter the wave speed yourself. The wavelength is still equal to the speed divided by the frequency.

At room temperature the speed of sound in air is about 343 meters per second while it's about 1481 meters per second in water. If a tower bell is rung at a frequency of 130 Hertz, then it produces sound waves with a wavelength of 343 divided by 130 which is approximately 2.64 meters.

3. Calculation based on energy of a photon

Light is also made up of a stream of particles called photons, each photon having an energy determined by its frequency. The Planck constant h relates these two quantities. So the wavelength can be calculated by multiplying h by c and then dividing by E, i.e. Wavelength = (h*c)/E.

The energy of a photon is usually given in electronvolts. A handy rule of thumb is that the wavelength (in nanometers) is roughly equal to 1240 divided by the energy (in electronvolts). So, for example, a photon with an energy of 2 electronvolts has a wavelength of about 620 nanometers and appears orange-red.

4. Backward calculation based on wavelength

If you know the wavelength already, then you can work backwards to find the frequency and photon energy. The frequency is equal to the speed of light divided by the wavelength, and the photon energy is equal to Planck's constant multiplied by this frequency.

So a wavelength of 500 nanometers converts to a frequency of about 600 terahertz and a photon energy of about 2.48 electron volts.

Electromagnetic spectrum

The wavelength range of the electromagnetic spectrum is extremely broad, from radio waves with lengths up to several thousand meters to gamma rays that are smaller than atoms. The various named frequency ranges overlap but generally the following boundaries are used.

Colors of visible light

The spectrum visible to the human eye ranges from about 380 nanometers to 700 nanometers. Shorter wavelengths appear violet and blue, while longer wavelengths are perceived as orange and red.

Examples for calculation:

These examples use this calculator's own formulas so that you can follow and verify the calculations step by step.

Units of wavelength:

Wavelength is a length and can therefore be expressed using any unit of length. Light and other short wavelength radiation are almost always quoted in nanometers or angstroms while radio waves are measured in meters.

How to use this calculator:

Start with the top menu and select the information you know. The input fields will change accordingly so that you always only see the required measurement values for the respective application case.

Enter known values to instantly calculate the wavelength. Each field has its own toggle for units, so you can enter frequencies in gigahertz or wavelengths in centimeters, for example. This calculator will do all of the necessary conversions for you.

In the light and inverse modes you can also set the refractive index to simulate how waves behave in water or glass. For vacuum or air just leave it at 1 as there is little difference.

Common mistakes:

The most common mistake is using the wrong speed. Electromagnetic waves travel at the speed of light, while sound and other mechanical waves are much slower. Mixing them up will result in answers that are off by a factor of a million or more. Use "Light" mode for electromagnetic waves, and "General Wave" mode for sound.

Another common mistake is forgetting that the frequency of a wave does not change when it enters a new medium. What changes are speed and wavelength, not frequency. This is why light retains its color underwater even though its wavelength becomes shorter.

This tool is for general education and solving everyday problems. For engineering, safety work or other high risk activities the values should be checked against the standards required by your particular project.