Wavenumber Calculator

What Is a Wavenumber Calculator?

A wavenumber describes how many wave cycles fit in a unit of distance, so it is the spatial frequency of a wave. The Wavenumber Calculator converts between wavelength and both common forms of wavenumber. It is used in spectroscopy, optics, and wave physics.

How the Math Works

The spectroscopic wavenumber is the reciprocal of the wavelength, while the angular wavenumber adds a factor of 2 pi:

$$\bar{\nu} = \frac{1}{\lambda}$$

$$k = \frac{2\pi}{\lambda} = 2\pi\bar{\nu}$$

Wavelength is converted to meters first. The spectroscopic wavenumber uses the reciprocal meter (m^-1), and one reciprocal centimeter (cm^-1) equals 100 m^-1.

Worked Example

Red light with a wavelength of 700 nm is 7 times 10 to the minus 7 meters. Then:

$$\bar{\nu} = \frac{1}{7 \times 10^{-7}} \approx 1.4286 \times 10^{6} \text{ m}^{-1}$$

$$k = \frac{2\pi}{7 \times 10^{-7}} \approx 8.9760 \times 10^{6} \text{ rad/m}$$

That spectroscopic wavenumber is about 14,285.7 cm^-1.

Related free tools

The Wave Speed Calculator links wavelength and frequency, the Wavelength Calculator solves related wave problems, and the Angular Frequency Calculator covers the time domain.