Wavelength Calculator

Enter a frequency or a wavelength and the other comes back, with the half and quarter wavelengths that actually show up in the physical world, the period, and for light the photon energy and its place in the spectrum. Pick light, sound, or supply your own wave speed.

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How this wavelength calculator works

Enter a frequency or a wavelength and the other one comes back, along with the half and quarter wavelengths, the period, and for light the photon energy and where it sits in the spectrum. The three buttons set the wave speed: light in a vacuum, sound in air, or anything you supply yourself.

Frequency and wavelength are not two properties of a wave. They are one property described two ways, tied together by how fast the wave travels, which is why fixing the speed means you can never choose both.

The formula

v = fλ
λ = v ÷ f
E = hf = hc ÷ λ
c = 299,792,458 m/s exactly
h = 6.62607015 × 10-34 J s exactly

v is the wave speed, f the frequency in hertz and λ the wavelength. Both constants above are exact by definition rather than measured: since 1983 the metre has been defined as the distance light travels in 1/299,792,458 of a second, and Planck's constant was fixed by definition in the 2019 revision of the SI. Measuring either one more precisely now measures your equipment rather than the universe.

Worked example

A microwave oven runs at 2.45 GHz. Its wavelength is 299,792,458 ÷ 2.45 × 109 = 12.24 cm, and the half-wavelength is 6.12 cm.

That second number is one you can go and measure. The waves bounce off the metal walls and set up a standing pattern, and the hot spots sit half a wavelength apart. Take the turntable out, lay a bar of chocolate or a tray of marshmallows flat inside, and heat it until the first few spots start to melt. The melted patches will be about 6 cm apart. Multiply that spacing by two, then by the 2.45 GHz printed on the back of the oven, and you have measured the speed of light in your kitchen to within a few percent.

It also explains the turntable. Without one, the cold spots stay cold, which is why a microwave with a broken turntable heats food unevenly rather than slowly. The oven is not weak, it is standing still.

Why 5 GHz Wi-Fi is worse through walls

Wi-Fi gives you the same physics in a decision you actually make. The 2.4 GHz band has a wavelength of 12.5 cm; the 5 GHz band is 6.0 cm. Longer waves diffract more readily around obstacles and lose less energy passing through ordinary building materials, so 2.4 GHz reaches further and through more walls. Shorter waves carry more bandwidth and face far less interference, because the 2.4 GHz band is shared with Bluetooth, cordless phones and, as above, your microwave oven.

So the trade is not a manufacturing compromise, it is the wave equation: range or bandwidth, pick one. The same rule sets everything else in the radio spectrum. AM radio at 1 MHz has a 300 m wavelength and bends over hills and around buildings, which is why it works in a valley. FM at 100 MHz has a 3 m wavelength, sounds far better and needs something close to line of sight. Submarines communicate at a few tens of hertz, wavelengths of thousands of kilometres, because those are the only waves that penetrate seawater, and the price is a data rate of a few characters per minute.

What the half and quarter wavelengths are for

The full wavelength is the number people ask for; the fractions are the numbers that show up in the physical world. Half a wavelength is the spacing of a standing wave's peaks, which is why the microwave's hot spots are 6 cm apart, why a room resonates at particular frequencies related to its dimensions, and why acoustic treatment is placed where it is. A quarter wavelength is the classic length for an antenna and for an absorber, because a wave reflecting off a hard surface returns a quarter wavelength out and cancels itself.

This is also why bass is so awkward indoors. A 40 Hz note has a wavelength of 8.6 m, longer than most rooms, so the room cannot support a full cycle and instead produces a lumpy pattern of loud and quiet spots. It is also why you cannot tell where a subwoofer is: locating a sound depends partly on the tiny arrival-time difference between your ears, and at wavelengths of several metres your head is far too small to register one. High frequencies are directional; low frequencies are everywhere.

Photons, and where light stops warming and starts breaking

For light there is a second equation running alongside, E = hf, and it explains something the wave picture cannot. Light delivers energy in individual packets whose size depends only on the frequency, not on the brightness. Infrared photons carry around 1 eV, visible light 2 to 3 eV, ultraviolet 3 to 12 eV, and X-rays thousands.

The threshold that matters is around 3 eV, roughly where violet gives way to ultraviolet, because that is where a single photon starts to carry enough energy to break a chemical bond. Below it, light mostly makes molecules jiggle, which is heat. Above it, light can rearrange them, which is sunburn, fading paint, and DNA damage. That is why an extremely bright red lamp will never give you sunburn while a weak ultraviolet one will: the bricks are the wrong size, and no amount of throwing more of them changes that. It is the observation that won Einstein his Nobel Prize, and it is sitting in the same two equations this page is built on.

Frequently asked questions

How do I convert frequency to wavelength?

Divide the wave speed by the frequency. For light that speed is 299,792,458 m/s, so a 2.45 GHz microwave has a wavelength of 12.24 cm. For sound in air at 20 degrees it is about 343 m/s, so a 440 Hz concert A has a wavelength of 78 cm. Frequency and wavelength are not two separate properties: they are one wave described two ways, and the speed ties them together.

What is the wavelength of Wi-Fi?

The 2.4 GHz band is 12.5 cm and the 5 GHz band is 6.0 cm. That difference is exactly why the two behave differently: longer waves diffract around obstacles and pass through walls with less loss, so 2.4 GHz reaches further, while shorter waves carry more bandwidth and meet far less interference. Range or bandwidth, and the wave equation makes you pick.

Why does a microwave oven have hot and cold spots?

Because the waves reflect off the metal walls and form a standing pattern whose peaks sit half a wavelength apart, which at 2.45 GHz is 6.12 cm. That is what the turntable exists to defeat. You can measure it: take the turntable out, heat a flat bar of chocolate until the first spots melt, and the melted patches will be about 6 cm apart. Double that spacing and multiply by 2.45 GHz and you have measured the speed of light in your kitchen.

What is the photon energy for a given wavelength?

E equals Planck's constant times frequency, or hc divided by wavelength. Visible light runs about 1.8 eV at the red end to 3.3 eV at the violet end. The threshold worth knowing is around 3 eV, because that is where a single photon starts to carry enough energy to break a chemical bond. Below it light mostly makes molecules jiggle, which is heat; above it light can rearrange them, which is sunburn and fading paint.

Why can I not tell where a subwoofer is?

Because locating a sound relies partly on the tiny difference in arrival time between your two ears, and at low frequencies the wavelength is far larger than your head. A 40 Hz note is 8.6 m long, so there is no meaningful difference for your brain to work with. High frequencies are directional and low ones are not, which is why a surround system can put the subwoofer anywhere and why bass sounds lumpy in a room smaller than its own wavelength.

What is the speed of sound and does it change?

About 343 m/s in air at 20 degrees Celsius, and yes, it changes. It rises roughly 0.6 m/s for every degree of temperature, so a cold room and a warm one differ by a few percent, and it is essentially independent of pressure, which surprises people. In water it is around 1,480 m/s and in steel about 5,000, which is why you can hear a train coming through the rail long before you hear it through the air.

Why is the speed of light exact rather than measured?

Because since 1983 the metre has been defined as the distance light travels in 1 divided by 299,792,458 of a second. The speed became a definition and the metre became the derived quantity, so measuring c more precisely now measures your ruler rather than the universe. Planck's constant got the same treatment in the 2019 revision of the SI, which is why both constants on this page are quoted without an uncertainty.

What is a quarter wavelength used for?

Antennas and absorbers, mostly. A wave reflecting off a hard surface travels a quarter wavelength out and a quarter back, arriving half a cycle late and cancelling itself, which is the basis of both a quarter-wave antenna and an acoustic absorber placed a quarter wavelength from a wall. Half a wavelength is the other useful fraction, being the spacing between the peaks of a standing wave, which is what sets a room's resonances and a microwave oven's hot spots.

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