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with wavelength λ, frequency ν, phase velocity of wave v_p, and angular frequency ω.

Less frequently it is defined simply as

One must be careful to note which definition is in use.

The wavenumber is closely related to the concept of the wave vector.

In the case of molecules, when an electron jumps from a higher orbit to a lower orbit energy is given out in the form of spectral lines. The wave number, of the emitted line for a hydrogen atom is given by

where λ is the wavelength, R is Rydberg constant, and are the orbit numbers, and is greater than .

Wavenumber in atmospheric science is defined as wavelength divided by the length of the spatial domain, or equivalently the number of times a wave has the same phase over the spatial domain. The domain might be 2π for the non-dimensional case, or

for an atmospheric wave , where R is Earth's radius and φ is latitude.

Wavenumber is the spatial analogue of frequency. Wavenumber and frequency can be obtained from grid point data by application of a Fourier transform in space or time, respectively. In the atmospheric sciences, wavenumber-frequency diagrams are a common way of visualizing atmospheric waves .