# Wavelength Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Aug 17, 2023

The wavelength calculator can assist you in determining the relationship between frequency and wavelength. Continue reading if you are here to learn how to calculate the frequency of a wave or look for the wavelength formula.

## Main properties of waves

There are three main properties of a wave: its velocity, wavelength, and frequency.

Wave velocity (v) is how fast a wave propagates in a given medium. Its unit is meter per second. Check the speed calculator for more information about speed and velocity.

Wavelength (λ) is the distance over which the shape of a wave repeats. It depends on the medium in which a wave travels. It is measured in meters.

Frequency (f) of a wave refers to how many times (per a given time duration) the particles of a medium vibrate when the wave passes through it. The unit of frequency is Hertz or 1/second.

## Wavelength formula

The relationship between wavelength and frequency is described by this simple equation:

λ = v/f

Remember about the proper units! If in trouble, you can always use the speed conversion.

## How to calculate wavelength

It's easy! Just use our wavelength calculator in the following way:

1. Determine the frequency of the wave. For example, f = 10 MHz. This frequency belongs to the radio waves spectrum.
2. Choose the velocity of the wave. As a default, our calculator uses a value of 299,792,458 m/s - the speed of light propagating in a vacuum.
3. Substitute these values into the wavelength equation λ = v/f.
4. Calculate the result. In this example, the wavelength will be equal to 29.98 m.
5. You can also use this tool as a frequency calculator. Simply type in the values of velocity and wavelength to obtain the result.

Remember that the frequency doesn't change when passing from one medium to another. If you are trying to solve a complex problem with more than one medium, use the wavelength formula again with the same frequency, but different velocity.

Waves with similar wavelengths produce easily recognizable beats. Here's our tool with which you can calculate the beat frequency. And we can also quantify the performance of our waves or signals using our modulation calculator.

## Typical wave speeds

You can find a few typical wave velocity values below. Type them into our wavelength calculator to learn what is, for example, the wavelength of red light in water.

• Light in air or vacuum: 299,792,458 m/s
• Light in water: 224,901,000 m/s
• Sound in air: 343.2 m/s
• Sound in water (20 °C): 1,481 m/s

## FAQ

### How does light wavelength affect photosynthesis?

The best wavelengths of light for photosynthesis are those that are blue (375-460 nm) and red (550-700 nm). These wavelengths are absorbed as they have the right amount of energy to excite electrons in the plant's pigments, the first step in photosynthesis. This is why plants appear green because red and blue light that hits them is absorbed!

### What is the relationship between frequency and wavelength?

Frequency (f) and wavelength (λ) are joined by the equation fλ = c, where c is the speed of light. As the speed of light is constant, if you increase the frequency, the wavelength must decrease to maintain this equation and vice versa. This means that the relationship between frequency and wavelength is inversely proportional.

### What color is the longest wavelength?

The color of the longest wavelength that we can see is red, with a wavelength of ~700 nm. The wave with the longest wavelength, radio waves, cannot be seen by the human eye, and therefore doesn't have a color. The color of the shortest wavelength is violet, at about 400 nm.

### How do you measure wavelength?

To measure a wavelength:

1. Use a photometer to measure the energy of a wave.
2. Convert the energy into joules (J).
3. Divide the energy by Planck’s constant, 6.626 × 10⁻³⁴ J⋅Hz⁻¹, to get the frequency of the wave.
4. Divide the speed of light, ~300,000,000 m/s, by the frequency to get wavelength.

### What is wavelength measured in?

Wavelength is the distance between two peaks (or troughs) of a wave, and is therefore measured in meters. Due to waves coming in all shapes and sizes, the prefix associated with meters can change dramatically, from km for radio waves, micrometers for visible light (although often given in nanometers), to picometers for gamma rays.

### How do you calculate energy from wavelength?

To estimate the energy:

1. Convert your wavelength into meters.
2. Divide the speed of light, ~300,000,000 m/s, by the wavelength in m. This gives you the wave's frequency.
3. Multiply the frequency by Planck’s constant, 6.626 × 10⁻³⁴ J⋅Hz⁻¹. The result is the waves energy in joules (J).

### How do you calculate wavelength from wavenumber?

To evaluate the wavelength:

1. Take your wavenumber, noting the units.
2. Divide 1 by the wavenumber.
3. It’s as easy as that!
4. The units for your new wavelength are 1 over the old units, so 1/cm becomes cm.
Bogna Szyk
Preset (optional)
light in vacuum
Wave velocity
m/s
Wave frequency
Hz
Wavelength (λ)
m
Wavenumber
1/
m
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