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Frequency to Wavenumber Converter
↔ Convert cm⁻¹ to Hz instead

Common Conversions

Hz cm⁻¹
29980000000 1
299800000000 10
2998000000000 100
14990000000000 500
29980000000000 1000
59960000000000 2000
89940000000000 3000
119900000000000 4000
149900000000000 5000
299800000000000 10000
599600000000000 20000
1499000000000000 50000

Why this conversion matters in chemistry

Frequency and wavenumber describe the same light, but spectroscopy strongly prefers wavenumber because it's proportional to photon energy. Raw frequency in hertz is what shows up in time-domain measurements, FTIR software outputs, or theoretical calculations — but by the time the result lands in a paper, it's in cm⁻¹. Divide the frequency in Hz by 2.998 × 10¹⁰ cm/s and you have your wavenumber. A C=O stretch at 5.1 × 10¹³ Hz becomes 1700 cm⁻¹, which is the number every organic chemistry textbook quotes. After enough spectra you stop thinking of them as two different scales; you just read one off the other.

Formula

cm⁻¹ = ν (Hz) ÷ c where c = 2.998 × 10¹⁰ cm/s; equivalently, cm⁻¹ ≈ Hz × 3.336 × 10⁻¹¹

Worked Examples

2.998×10¹³ Hz = 1000 cm⁻¹

Mid-IR, right in the fingerprint region. About 30 THz — a clean anchor worth remembering for spectral bookkeeping.

8.994×10¹³ Hz = 3000 cm⁻¹

The C–H stretching region. Any aliphatic spectrum has peaks clustered around here.

5.097×10¹³ Hz = 1700 cm⁻¹

A generic carbonyl C=O stretch. Exact position shifts with context — aldehydes sit near 1725 cm⁻¹, ketones 1715, esters 1735, amides 1650–1680 — and that sensitivity is exactly what makes the band so diagnostic.

2.998×10¹² Hz = 100 cm⁻¹

Far-IR, or what physics labs call the terahertz range. Low-energy lattice vibrations and some metal-ligand stretches live out here.

Frequently Asked Questions

How do I convert frequency to wavenumber?
Divide by the speed of light in cm/s (c = 2.998 × 10¹⁰ cm/s). Or, shortcut: multiply by about 3.336 × 10⁻¹¹. A C–H stretch at 9 × 10¹³ Hz works out to roughly 3000 cm⁻¹, which is why spectroscopists quote the wavenumber directly — it's easier to read and compare than the raw THz-range frequency.
Why does wavenumber line up with photon energy?
Because E = hν = hc/λ = hcν̃. Planck's constant and the speed of light are both fixed, so wavenumber differs from energy only by constant factors. A peak at 3000 cm⁻¹ carries exactly twice the photon energy of one at 1500 cm⁻¹. That's what makes cm⁻¹ such a natural spectroscopy axis: the number on the axis already reflects the physics you care about.
How do ν̃, λ, and ν relate?
ν̃ = 1/λ when λ is in centimeters, ν = c/λ, and ν = c × ν̃. All three describe the same wave, just indexed differently. Most people find it easier to keep one of the three straight and derive the others on demand than to memorize all three independently.