Wavenumber to Wavelength Converter
Common Conversions
| cm⁻¹ | nm |
|---|---|
| 100 | 100000 |
| 250 | 40000 |
| 500 | 20000 |
| 1000 | 10000 |
| 1500 | 6666.7 |
| 2000 | 5000 |
| 2500 | 4000 |
| 3000 | 3333.3 |
| 3500 | 2857.1 |
| 4000 | 2500 |
| 5000 | 2000 |
| 10000 | 1000 |
Why this conversion matters in chemistry
IR spectra are almost always plotted against wavenumber, but the wavelength form still matters when you're choosing sample cells or sample-preparation windows — a 1650 cm⁻¹ amide-I band in a protein spectrum corresponds to 6.06 µm, which is well inside the transparency range of CaF₂ windows but outside that of common glass. A C–H stretch at 3000 cm⁻¹ is 3.33 µm; a C=O at 1700 cm⁻¹ is 5.88 µm. Dividing 10⁷ by the wavenumber in cm⁻¹ gives you the wavelength in nm, and shifting the decimal by three converts to µm — the native unit of IR optics specifications.
Formula
Where the factor comes from
This conversion is its own inverse, which is rare enough to be worth noticing: λ(nm) = 10⁷ ÷ ν̃(cm⁻¹) uses precisely the constant that carries wavelength back the other way, so forward and reverse are the same keystroke. The reason is that both units are reciprocal statements about a single wave, and the only thing standing between them is the prefix ratio. A centimeter is 10⁻² m and a nanometer is 10⁻⁹ m, so a centimeter holds 10⁷ nanometers — a defined multiplier, exact, with no measurement anywhere inside it. Put 10⁴ in the numerator instead of 10⁷ and the answer arrives in micrometers, which is the version worth committing to memory, because infrared windows, filters and detector cutoffs are specified in µm while the spectrum itself is plotted in cm⁻¹.
Precision and significant figures
The division will happily produce digits the spectrum never contained. A band picked off a survey scan taken at 4 cm⁻¹ resolution and reported as 3333.3 nm claims five figures, while 4 cm⁻¹ at that position spans about 4.4 nm — so 3333 nm, or better 3.33 µm, is as far as the data reaches. Precision degrades sharply toward the far infrared, where that same 4 cm⁻¹ near 500 cm⁻¹ opens out to roughly 160 nm. Three figures is the usual honest ceiling anywhere in the mid-IR. Optics catalogues quote transmission ranges in micrometers to two or three figures for exactly this reason.
Worked Examples
10 µm — solidly in the mid-IR fingerprint region, where most diagnostic bands live.
3.33 µm. The C–H stretching region — almost any aliphatic organic spectrum shows peaks here.
5.88 µm. The carbonyl C=O region — one of the most diagnostic features of organic IR spectra.
20 µm — far-IR territory, where lattice vibrations and some metal-ligand modes appear.
Common mistakes
Inverting a Raman shift directly
Raman spectra are plotted as a displacement from the excitation line, not as an absolute position, so a 1000 cm⁻¹ shift is emphatically not light at 10 µm. Subtract it from the laser's own wavenumber first: 532 nm sits at 18,797 cm⁻¹, so the Stokes photon departs at 17,797 cm⁻¹, which is 562 nm — 30 nm from where the laser started.
Treating a splitting in nm as portable
Wavenumber differences mean the same thing across the whole spectrum; the wavelength differences they map onto do not. A 20 cm⁻¹ separation between two bands spans about 22 nm up at 3000 cm⁻¹ but about 770 nm down at 500 cm⁻¹. Quote splittings and solvent shifts in cm⁻¹, where one number keeps one meaning wherever it lands.
Forgetting the wavelength is a vacuum value
Wavenumber is referenced to vacuum, so the wavelength coming out is a vacuum wavelength. Inside an ATR crystal the wave is shorter by the crystal's refractive index — roughly a factor of 2.4 for zinc selenide across the mid-infrared — and it is that shortened wavelength, not the vacuum figure, that governs how far the evanescent field reaches into the sample.