Wavelength to Wavenumber Converter
Common Conversions
| nm | cm⁻¹ |
|---|---|
| 200 | 50000 |
| 250 | 40000 |
| 400 | 25000 |
| 500 | 20000 |
| 700 | 14286 |
| 1000 | 10000 |
| 2500 | 4000 |
| 5000 | 2000 |
| 10000 | 1000 |
| 20000 | 500 |
| 50000 | 200 |
| 100000 | 100 |
Why this conversion matters in chemistry
IR spectra get plotted against wavenumber — cm⁻¹ — almost universally, even when the underlying instrument records wavelength. The reason is physical: wavenumber is directly proportional to photon energy (E = hcν̃), so the axis actually corresponds to something molecules care about. A 3.33 µm (3333 nm) C–H stretch shows up at 3000 cm⁻¹; a 10 µm C–O stretch lands at 1000 cm⁻¹; the fingerprint region runs roughly 400 to 1500 cm⁻¹. The conversion is one over the wavelength, expressed in centimeters — divide 10⁷ by your wavelength in nanometers and you're done.
Formula
Where the factor comes from
Unusually for a spectroscopic conversion, no physical constant appears anywhere in it. Wavenumber is defined as the reciprocal of wavelength, and the entire factor comes out of the two prefixes: centi is 10⁻², nano is 10⁻⁹, so one centimeter contains exactly 10⁷ nanometers. Write the wavelength in centimeters, take the reciprocal, and the arithmetic collapses to ν̃(cm⁻¹) = 10⁷ ÷ λ(nm). Both prefixes are defined multipliers, so the 10⁷ is exact and the speed of light stays out of it entirely. One caveat sits underneath. The strict definition of spectroscopic wavenumber is ν/c, referenced to vacuum, and 1/λ reproduces that only when λ is itself a vacuum wavelength — which is why published band positions are vacuum values even when the instrument looked through air.
Precision and significant figures
Relative precision survives the reciprocal untouched; absolute precision does not. Differentiating gives δν̃ = δλ × 10⁷/λ², so a fixed ±1 nm uncertainty is worth ±250 cm⁻¹ at 200 nm and only ±2.5 cm⁻¹ at 2000 nm. One instrument specification therefore means wildly different things at the two ends of its range, and a wavenumber quoted to the nearest unit in the deep UV claims a wavelength read far finer than any monochromator delivers. Carry the three or four figures the wavelength justified rather than whatever the division happens to produce. The 10⁷ is exact and never limits anything, so every digit in the answer traces back to the input.
Worked Examples
Green light, right in the middle of the visible. UV-Vis spectra are usually plotted in nm, but the wavenumber is useful for comparing transitions across spectral regions.
Ten microns — smack in the IR fingerprint region, where most diagnostic vibrational modes live.
UV territory. Common for aromatic π→π* transitions and the upper end of DNA absorbance.
A round anchor in the near-IR — well past the red end of the visible range, in the region near-IR spectroscopy and many fiber-optic systems work in.
Common mistakes
The exponent depends on the input prefix
10⁷ belongs to nanometers alone. Micrometers take 10⁴ and ångströms take 10⁸, and the ångström slip is the treacherous one: a 3.33 µm C–H stretch entered as 33,300 Å and run through the 10⁷ rule gives 10⁷ ÷ 33,300 = 300 cm⁻¹, a plausible far-IR number that is wrong by a factor of ten. The band is at 3000 cm⁻¹.
Even spacing in nm is uneven in cm⁻¹
A detector sampling at a constant nanometer step yields points that crowd together at low wavenumber and spread apart at high wavenumber once converted. Subtracting or co-adding spectra whose axes came from different conventions then compares points that do not line up. Interpolate everything onto a common wavenumber grid first, and do the arithmetic afterwards.
Reciprocal meters exported as reciprocal centimeters
Strict SI reporting and some export routines use m⁻¹, which differs from cm⁻¹ by exactly a factor of one hundred — 3000 cm⁻¹ is 300,000 m⁻¹. A file arriving with an axis that runs to a few hundred thousand is almost certainly in m⁻¹, and feeding it to peak-assignment software configured for cm⁻¹ displaces every band by two decades.