Tool · Units and conversions

Wavelength Calculator

Enter a wavelength, frequency, photon energy or wavenumber 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

Enter a wavelength, frequency, photon energy or wavenumber

Refractive index of the medium n

Wavelengths are vacuum wavelengths. Air has n = 1.00027 near 1550 nm, which shifts the wavelength by about 0.4 nm; water is about 1.33 and ordinary glass about 1.5.

Presets

Any wave

Wave speed v (m/s)

Frequency f

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.

Check	Expected	Computed	Tolerance

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 $\lambda$ 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:

\lambda = \frac{v}{f}, \qquad \lambda_0 = \frac{c}{\nu}, \qquad E = h\nu = \frac{hc}{\lambda_0}, \qquad \tilde\nu = \frac{1}{\lambda_0}

with $c$ = 299,792,458 m/s and $h$ = 6.62607015 × 10⁻³⁴ J·s, both exact. In convenient units, $E\,[\mathrm{eV}] = 1239.84/\lambda_0\,[\mathrm{nm}]$ and $\tilde\nu\,[\mathrm{cm^{-1}}] = 10^7/\lambda_0\,[\mathrm{nm}]$ . 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 $\lambda_0/n$ . Laser and spectrometer wavelengths are quoted in vacuum unless marked as air wavelengths. 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.

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. D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics (Wiley).