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Wavelength Calculator

Use this free wavelength calculator to convert between frequency, wavelength, and photon energy in seconds. Pick a mode — frequency to wavelength, wavelength to frequency, or energy to wavelength — choose the medium, and the calculator shows the answer in the units you want, with every step of the working so you can check it or use it for homework.

How it works

Every wave has three linked properties: how fast it travels, how often it repeats, and how long one repeat is. The speed is fixed by the medium, the frequency counts how many wave cycles pass each second, and the wavelength is the physical length of one cycle. Because speed equals frequency times wavelength, knowing any two of them tells you the third. For light, the speed in a vacuum is one of nature's constants: 299,792,458 meters per second, usually rounded to 3 × 10⁸ m/s.

The medium matters because light slows down when it enters a denser material. In air the speed is 299,702,547 m/s, only a tiny fraction slower than a vacuum, so wavelengths in air are almost identical to vacuum values. In water the speed drops to about 225,000,000 m/s, roughly 75 percent of the vacuum speed, so the same frequency produces a wavelength only three-quarters as long. The frequency itself never changes when light crosses into a new medium — only the speed and the wavelength change together.

Units are where most mistakes happen, so the calculator handles them for you. Frequencies run from hertz up to terahertz: 1 kHz is 1,000 Hz, 1 MHz is 1,000,000 Hz, 1 GHz is 1,000,000,000 Hz, and 1 THz is 1,000,000,000,000 Hz. Wavelengths run the other way, from meters down to nanometers: 1 cm is 0.01 m, 1 mm is 0.001 m, 1 micrometer (µm) is 0.000001 m, and 1 nanometer is 0.000000001 m. Radio waves are meters long, while visible light is only 400 to 700 nanometers.

The third mode uses the photon picture of light. Each photon carries an energy that depends only on its frequency: E = hf, where h is Planck's constant, 6.626 × 10⁻³⁴ joule-seconds. Combining that with λ = c / f gives E = hc / λ, so a shorter wavelength means a more energetic photon. A handy shortcut is that wavelength in nanometers is about 1239.84 divided by the energy in electronvolts (eV), the unit physicists use for single photons. That is why ultraviolet light, with wavelengths under 400 nm, carries enough energy per photon to damage skin, while infrared light above 700 nm carries less.

The same formula also covers sound and other waves if you swap in the right speed — about 343 m/s for sound in air — but this calculator is set up for light, so its media are vacuum, air, and water. Try the presets: an FM radio station at 100 MHz has a wavelength of about 3 meters, which is why FM antennas are roughly a meter or two long, while a Wi-Fi signal at 2.4 GHz has a wavelength of about 12.5 centimeters.

Worked example

An FM radio station broadcasts at 100 MHz. What is its wavelength in a vacuum, and what frequency is green light with a wavelength of 500 nanometers?

Step 1: Convert the frequency to hertz — 100 MHz = 100 × 1,000,000 = 100,000,000 Hz.
Step 2: Divide the speed of light by the frequency — λ = 299,792,458 / 100,000,000 = 2.9979 m, about 3 meters.
Step 3: For the green light, convert the wavelength to meters — 500 nm = 500 × 10⁻⁹ = 0.0000005 m.
Step 4: Divide the speed of light by the wavelength — f = 299,792,458 / 0.0000005 = 599,584,916,000,000 Hz = 599.58 THz.
Step 5: Check with photon energy — E = 1239.84 / 500 = 2.48 eV, so a green photon carries about 2.48 electronvolts.

Enter 100 with MHz selected and "Frequency → Wavelength" in the calculator and it gives exactly the same result: λ = 2.9979 m. Switch to "Wavelength → Frequency", enter 500 nm, and it gives 599.58 THz. Try the water medium too: the same 100 MHz wave in water has a wavelength of only 2.25 m.

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