What this calculator does
Wavenumber and wavelength describe the same wave from two different angles. Wavelength is the physical distance between successive peaks of a wave, while wavenumber counts how many of those wave cycles fit into a fixed length, most commonly one centimetre. Spectroscopy, chemistry and infrared analysis usually report results as wavenumber rather than wavelength, because it scales directly with energy and frequency, making spectra easier to read and compare.
This calculator uses the spectroscopic convention, wavenumber = 1 ÷ wavelength, expressed in inverse centimetres (cm⁻¹). This is distinct from the angular wavenumber used in some physics contexts, which instead uses 2π ÷ wavelength; the spectroscopic convention is the one seen on infrared spectra, Raman shift tables and most chemistry reference material, which is why it is used here.
The formula
Wavenumber in cm⁻¹ equals 10,000,000 divided by wavelength in nanometres, since one centimetre is 10 million nanometres. Converting the other way, wavelength in nanometres equals 10,000,000 divided by wavenumber in cm⁻¹. The relationship is symmetric, so the same formula runs in either direction depending on which value is known.
| Term | Meaning |
|---|---|
| Wavelength (λ) | The physical distance between successive peaks of a wave, usually given in nanometres for visible and near-visible light. |
| Wavenumber (ṽ) | The number of wave cycles per centimetre, ṽ = 1/λ (spectroscopic convention), usually given in cm⁻¹. |
| Spectroscopic convention | The convention used in chemistry and spectroscopy, distinct from the angular wavenumber (2π/λ) used in some physics contexts. |
The inputs explained
| Field | What to enter |
|---|---|
| Convert | Choose from Wavelength → wavenumber, Wavenumber → wavelength. |
| Wavelength (wavelength mode) (nm) | Enter a wavelength when converting from wavelength to wavenumber. |
| Wavenumber (wavenumber mode) (cm⁻¹) | Enter a wavenumber when converting from wavenumber to wavelength. |
When to use it
Reading an infrared spectrum
Infrared spectra are plotted against wavenumber, typically from around 4000 down to 400 cm⁻¹, because absorption bands for particular bond types fall at roughly fixed wavenumber positions regardless of the rest of the molecule.
Comparing a spectroscopy result to a wavelength-based figure
A supplier or instrument might quote a laser or filter by wavelength in nanometres, while a related dataset uses wavenumber. Converting one to the other puts both readings on the same footing.
Working out Raman shift or absorption band positions
Raman spectroscopy reports shifts directly in wavenumber terms; converting a known excitation wavelength to wavenumber is often the first step before working out where a scattered peak should fall.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Wavenumber for common visible and near-visible wavelengths
A range of wavelengths across the visible spectrum, converted to spectroscopic wavenumber.
| Wavelength | Wavenumber |
|---|---|
| 200 nm | 50,000.0 cm⁻¹ |
| 400 nm | 25,000.0 cm⁻¹ |
| 500 nm | 20,000.0 cm⁻¹ |
| 700 nm | 14,285.7 cm⁻¹ |
| 1000 nm | 10,000.0 cm⁻¹ |
| 2000 nm | 5,000.0 cm⁻¹ |
Wavelength for common infrared wavenumbers
A range of wavenumbers typical of infrared spectroscopy, converted back to wavelength.
| Wavenumber | Wavelength |
|---|---|
| 5,000 cm⁻¹ | 2,000.0 nm |
| 10,000 cm⁻¹ | 1,000.0 nm |
| 15,000 cm⁻¹ | 666.7 nm |
| 20,000 cm⁻¹ | 500.0 nm |
| 30,000 cm⁻¹ | 333.3 nm |
| 50,000 cm⁻¹ | 200.0 nm |
Questions
Is this the same wavenumber used in physics wave equations?
Not always. This calculator uses the spectroscopic convention (ṽ = 1/λ, in cm⁻¹), standard in chemistry and infrared spectroscopy. Some physics contexts instead use the angular wavenumber k = 2π/λ, which is larger by a factor of 2π and usually expressed in radians per metre.
Why is wavenumber usually given in cm⁻¹ rather than m⁻¹?
Inverse centimetres keep typical infrared and visible-light wavenumbers in a convenient range, roughly hundreds to tens of thousands, rather than the much larger numbers that would result from using inverse metres. It is simply the historical and continuing convention in spectroscopy.
How does wavenumber relate to photon energy?
Wavenumber is directly proportional to photon energy and frequency: a higher wavenumber means a shorter wavelength, a higher frequency and a more energetic photon. This is why infrared spectra are often read directly in wavenumber rather than converting to wavelength first.
What wavenumber range does visible light cover?
Visible light spans roughly 700 nm (red) to 400 nm (violet), which corresponds to a wavenumber range of approximately 14,300 to 25,000 cm⁻¹.
For the direct relationship between wave speed, frequency and wavelength, see the wave speed, frequency and wavelength calculator. To convert a wavelength into a single photon's energy, see the photon energy calculator.