Wavenumber Calculator

Find the wavenumber of a wave from its wavelength.

Angular wavenumber (rad/m) 12,566,370.61

Spectroscopic wavenumber (1/cm) 20,000

Formula: k = 2π ÷ λ; ν̃ = 1 ÷ λ

Step-by-step with your numbers:

1. Values used:

2. Wavelength = 500 nm

4. Angular wavenumber = 12,566,370.61rad/m

5. Spectroscopic wavenumber = 20,0001/cm

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Wavenumber counts how many wave cycles fit per unit length.

The math behind it

The angular wavenumber is k = 2π/λ (rad/m); spectroscopists use ν̃ = 1/λ in cm⁻¹.

500 nm → k ≈ 1.26 × 10⁷ rad/m (20,000 cm⁻¹).

Why use cm⁻¹ in spectroscopy?

It's proportional to photon energy and gives convenient numbers for molecules.