Tool · Units and conversions

Wavelength Calculator

What frequency, photon energy and wavenumber does a given wavelength have, and where does it sit in the spectrum? Enter any one of the four and the calculator gives the other three, the period, the wavelength inside a medium of any refractive index, and the region of the spectrum. A second panel applies the wavelength formula to sound or any other wave. Background: wavelength, frequency and wavenumber, photon energy, refractive index, and infrared bands.

Light
Wavelengths entered here are vacuum wavelengths. Line tables often quote air wavelengths, which are shorter by the index of air: n = 1.00028 at 633 nm, so the helium-neon line is 632.991 nm in vacuum and 632.816 nm in air; set the medium index to 1.0002765 to see the air value. Water is about 1.33 and ordinary glass about 1.5.
Presets
Any wave
The wavelength formula λ = v/f holds for sound, water waves and radio: the wavelength is the distance the wave travels in one period.
Readouts
Where it sits in the electromagnetic spectrum
Learn with it

Three short experiments. Each one sets the inputs, says where to look, and asks for a prediction before it shows the result.

Checked against

These checks run in your browser on every load. Each conversion is compared with a value worked out by hand from the exact SI constants, and a wavelength is carried to frequency, energy and wavenumber and back.

CheckExpectedComputedTolerance

The constants are c = 299,792,458 m/s, h = 6.62607015 × 10−34 J·s and e = 1.602176634 × 10−19 C, all exact since the 2019 SI revision. The tolerance is the largest relative difference from Expected that still passes.

The model

The wavelength formula relates the wavelength λ of any wave to its speed v and frequency f: in one period the wave advances by one wavelength. For light in vacuum the speed is c, and the photon energy follows from Planck’s constant:

λ=vf,λ0=cν,E=hν=hcλ0,ν~=1λ0

with c = 299,792,458 m/s and h = 6.62607015 × 10−34 J·s, both exact. In convenient units, E [eV]=1239.84/λ0 [nm] and ν~ [cm−1]=107/λ0 [nm]. In a medium of refractive index n light travels at c/n; its frequency and photon energy are fixed by the source, so the wavelength becomes λ0/n. The calculator takes every wavelength as a vacuum wavelength. Telecom grids and most near-infrared laser datasheets quote vacuum values, while spectroscopic line tables and many spectrometer calibrations quote air wavelengths between 200 nm and 2 µm, shorter by the index of standard air, about 1.00028 at 633 nm (Edlén, 1966). The helium-neon line, usually quoted as 632.8 nm, is 632.816 nm in air and 632.991 nm in vacuum; read as a vacuum value, 632.8 nm would put the wavenumber 4.8 cm−1 too high. The presets use vacuum values, and setting the medium index to the air index converts one into the other. The index is taken as a single number; in a real material it depends on wavelength, which the refractive index calculator gives from Sellmeier data. To measure a vacuum wavelength to many digits, see wavemeter.

Worked example

Telecom light at 1550 nm has a frequency of 193.41 THz, a period of 5.1702 fs, a wavenumber of 6451.6 cm−1 and a photon energy of 0.7999 eV. In silica fiber, with n about 1.444, the wavelength inside the glass is 1073.4 nm. For sound in air at 343 m/s, the note A at 440 Hz has a wavelength of 77.95 cm.

For power in dBm, linewidths in GHz and nm, and photon flux, see the photonics unit converter.

References: BIPM, The International System of Units (SI brochure), 9th ed. (2019). ISO 21348:2007, Space environment: Process for determining solar irradiances. ISO 20473:2007, Optics and photonics: Spectral bands. CIE S 017:2020, International Lighting Vocabulary. B. Edlén, The refractive index of air, Metrologia 2, 71–80 (1966). D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics (Wiley).