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

Common Conversions

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

Why this conversion matters in chemistry

Wavenumber is what spectroscopy reports because it's proportional to energy and reads cleanly in the IR range. Frequency in hertz is what the underlying physics wants — photon energy is E = hν, force-constant calculations are built around vibrational frequencies, quantum-mechanical models return frequencies directly. Multiplying cm⁻¹ by the speed of light in cm/s (2.998 × 10¹⁰ cm/s) converts one to the other. A 1650 cm⁻¹ amide-I C=O stretch becomes 4.95 × 10¹³ Hz, or 49.5 THz. The step shows up every time a molecular dynamics simulation or ab initio calculation outputs vibrational frequencies and you need to compare them against an experimental spectrum.

Formula

Hz = cm⁻¹ × c = cm⁻¹ × 2.998 × 10¹⁰

Worked Examples

1000 cm⁻¹ = 2.998×10¹³ Hz

Mid-IR fingerprint region. Roughly 30 THz — a clean anchor worth remembering for spectral bookkeeping.

3000 cm⁻¹ = 8.994×10¹³ Hz

C–H stretching region. Any aliphatic spectrum shows peaks clustered here.

1700 cm⁻¹ = 5.097×10¹³ Hz

A generic carbonyl C=O stretch. The exact position shifts with chemical context — aldehydes near 1725, ketones 1715, esters 1735, amides 1650–1680 — which is what makes the band so diagnostic.

100 cm⁻¹ = 2.998×10¹² Hz

Far-IR / THz range. Low-energy lattice vibrations and some metal-ligand modes live here.

Frequently Asked Questions

How do I convert wavenumber to frequency?
Multiply by the speed of light expressed in cm/s: ν = ν̃ × 2.998 × 10¹⁰ Hz. So 1000 cm⁻¹ is 3.00 × 10¹³ Hz, and 3000 cm⁻¹ is 9.00 × 10¹³ Hz. The factor is just the speed of light — it's what's needed to bridge the centimeter-indexed wavenumber and the second-indexed frequency.
How do ν̃, λ, and ν all relate?
ν̃ = 1/λ when λ is in centimeters, ν = c/λ, and ν = c × ν̃. The three quantities describe the same wave through different indices: inverse length, length, and time. Most people find it easier to keep one in their head and derive the others on demand.
What frequency ranges do IR absorptions span?
The mid-IR band (400–4000 cm⁻¹) corresponds to roughly 1.2 × 10¹³ to 1.2 × 10¹⁴ Hz — the low end of the terahertz band through mid-infrared. Near-IR sits above that and far-IR below. Most diagnostic vibrational bands fall in the mid-IR.