Wave Number Calculator

Work out wave number instantly with clear inputs, formula shown and shareable results.

About Wave Number Calculator

Wave number counts cycles per unit length, so it is the reciprocal of wavelength. Physicists usually mean the angular form 2pi/lambda, while spectroscopists mean 1/lambda and quote it in reciprocal centimetres. A 500 nm wave is 2.0e6 per metre, or 20,000 cm-1, and 1.26e7 rad/m in angular terms.

Formulas

Angular wave number

k = 2 pi / lambda

Spectroscopic wave number

nu-bar = 1 / lambda, usually in cm-1

Worked example

With the default values below, Wave Number Calculator returns Wave Number of 1.25664 × 10⁷. Change any input above and every figure here is recalculated in your browser.

Inputs used

Wavelengthminimum 0 m: 0.000001 m
Which wave numberone of Angular wave number k = 2pi/lambda, Spectroscopic wave number 1/lambda: Angular wave number k = 2pi/lambda

Results

Wave Number: 1.25664 × 10⁷ 1/m
Spectroscopic Wave Number: 2.0000 × 10⁶ 1/m
Wave Number In Reciprocal Centimetres: 20,000.000 1/cm
Angular Wave Number: 1.2566 × 10⁷ rad/m

Step by step

1Values used
2Angular wave number
3Spectroscopic wave number
4Wave Number= 12,566,400.00000 1/m
5Spectroscopic Wave Number= 2,000,000.0000 1/m
6Wave Number In Reciprocal Centimetres= 20,000.000 1/cm
7Angular Wave Number= 12,566,400.0000 rad/m

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do spectroscopists use cm-1?

Because it is proportional to photon energy and gives convenient numbers - the infrared fingerprint region runs 400-4000 cm-1.

Which convention is right?

Both, in their own field. The factor of 2pi between them is why the units are quoted as rad/m for the angular form.