Wavelength Calculator
Calculate wavelength from wave speed and frequency, with optional presets for common waves. Useful for converting between meters and smaller units.
Wavelength Calculator
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What the wavelength calculator does
Every wave has a length, the distance over which its pattern repeats. This calculator finds that wavelength from the wave's speed and its frequency, and it works for any kind of wave, with built-in speeds for light and sound in different materials. It also reports the wave number.
Below is what wavelength is, the equation behind it, how it relates to frequency, and a worked example.
How to use it
- Pick a preset medium to fill in the wave speed, or enter your own wave velocity.
- Enter the wave frequency, with its unit.
- Press Calculate for the wavelength and wave number, or Reset to clear them.
What wavelength is
A wave is a repeating disturbance that travels through space, and its wavelength is the distance between one peak and the next, the length of a single cycle of the pattern. For ripples on a pond it is the spacing between crests; for sound it is the distance between successive compressions of the air; for light it is the spacing of the electromagnetic oscillation, which sets the colour we see.
Wavelength is one of the most important properties of a wave because it shapes how the wave behaves. It determines the colour of light and the pitch of sound, governs how a wave bends around obstacles and spreads through openings, and decides whether a wave passes through a gap or is blocked by it. From radio broadcasting to the colours of a rainbow, wavelength is the quantity that tells you what kind of wave you are dealing with, and this calculator works it out.
The equation it uses
Wavelength is the wave's speed divided by its frequency:
λ = v ÷ f
Here λ is the wavelength, v is the speed at which the wave travels through its medium, and f is the frequency, the number of cycles passing a point each second. The logic is simple: in one second the wave advances a distance equal to its speed, and that distance is filled with as many cycles as the frequency, so dividing the speed by the frequency gives the length of a single cycle. The calculator takes the speed from your chosen medium and divides by the frequency you enter.
The inverse link to frequency
For a wave travelling at a fixed speed, wavelength and frequency are inversely related: as one rises, the other falls. A high-frequency wave packs many cycles into each second, so each cycle is short and the wavelength is small. A low-frequency wave has long, lazy cycles and a long wavelength. They are two ways of describing the same wave, tied together by its speed.
This inverse relationship is why high-pitched sounds have short wavelengths and low-pitched ones long, and why blue light, at the high-frequency end of the visible spectrum, has a shorter wavelength than red. It also means the speed of the wave matters: the same frequency gives a different wavelength in a different medium, since the wave travels at a different speed. That is why the calculator lets you choose the medium, and why a sound of fixed frequency has a far longer wavelength in water than in air.
The wave number
Alongside the wavelength, the calculator reports the wave number, which is simply one divided by the wavelength. Where the wavelength tells you how long one cycle is, the wave number tells you how many cycles fit into a unit of distance, so it is a kind of spatial frequency, the counterpart in space to what frequency is in time.
The wave number is widely used in optics and spectroscopy, where it is often more convenient than the wavelength itself, because it rises in step with energy and frequency rather than falling. A larger wave number means a shorter wavelength and a more energetic wave. The calculator provides it so that you can work in whichever description suits your problem, the length of a cycle or the number of cycles per unit length.
Units and precision
The calculator works in SI units underneath, with speed in metres per second and frequency in hertz, and it reports the wavelength across a range of length units from nanometres to kilometres, with the wave number in inverse length. The medium presets carry the standard speeds of light and sound in various materials, and you can enter a custom speed for any other wave. Results carry several significant figures.
A worked example
Take green light, which has a frequency of about 540 terahertz, travelling at the speed of light in vacuum.
The wavelength is λ = v ÷ f = 299,792,458 ÷ (540 × 10¹²) ≈ 555 nanometres, squarely in the green part of the visible spectrum, which is why this frequency looks green to the eye. A lower-frequency red light would come out with a longer wavelength, around 700 nanometres, and a higher-frequency blue light with a shorter one.
Questions people ask
How do you calculate wavelength?
Divide the wave's speed by its frequency, λ = v/f. The speed depends on the medium, and the frequency is the number of cycles per second.
How are wavelength and frequency related?
Inversely, for a fixed wave speed. Higher frequency means shorter wavelength, and lower frequency means longer wavelength, since they are tied together by the speed.
Does wavelength change with the medium?
Yes. The same frequency gives a different wavelength in a different medium, because the wave travels at a different speed. A sound has a much longer wavelength in water than in air.
What is the wave number?
One divided by the wavelength, a measure of how many cycles fit into a unit of distance. It is a spatial frequency, often used in optics and spectroscopy, and rises as the wavelength shortens.
References
A quick note on where the physics comes from. The wave relationship linking speed, frequency, and wavelength is standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The SI units follow the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.
- OpenStax, University Physics Volume 1, Section 16.1, Traveling Waves. https://openstax.org/books/university-physics-volume-1/pages/16-1-traveling-waves
- HyperPhysics, Wavelength and Wave Relationship. http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/wavms.html
- National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811
Bibek Lal Karna is a PhD student and graduate teaching assistant at the University of Mississippi, with deep interests in theoretical and gravitational physics. He is also the founder of NRCC and is strongly engaged in scientific teaching and communication. At Eon Tools, he reviews physics tools.