Wavelength to wavenumber converter

Enter a value in either field. The values are inversely related.
Standard formula: Wavenumber = 10⁷ / Wavelength (nm).

Wavelength

⇌

Wavenumber

cm⁻¹

Clear Fields

ṽ = 10^7 / λ

Enter a value to calculate.

How it works?

Wavelength ($\lambda$) represents the distance between wave peaks. Wavenumber ($\tilde{\nu}$) is the inverse: the number of waves that fit into a set distance (usually 1 centimeter).

$$ \tilde{\nu} = \frac{1}{\lambda_{(\text{cm})}} $$ Basic Definition

$$ \tilde{\nu} = \frac{10^7}{\lambda_{(\text{nm})}} $$ From Nanometers

Where:

$\tilde{\nu}$ : Wavenumber (cm⁻¹). Standard for IR Spectroscopy.
$\lambda$ : Wavelength (nm). Standard for UV-Vis/Telecom.
10^7 : Unit conversion factor (nm to cm).

Note: High energy = Short wavelength = High wavenumber. (e.g., 1000 nm = 10,000 cm⁻¹).

Converting Wavenumber back to Wavelength

While spectrometers record data in Wavenumbers (cm⁻¹) to keep energy scales linear, engineers building the actual detectors and lasers need to know the physical **Wavelength (nm)**. This calculator bridges the gap between the "chemical fingerprint" and the hardware used to detect it.

Infrared Bands Reference

Common molecular vibration bands and their physical wavelengths.

Vibration / Band	Wavenumber (cm⁻¹)	Wavelength (nm / µm)
Hydroxyl (O-H) Stretch	~3,600 cm⁻¹	2,777 nm (2.7 µm)
Alkane (C-H) Stretch	~2,950 cm⁻¹	3,389 nm (3.4 µm)
Carbon Dioxide (CO₂)	~2,350 cm⁻¹	4,255 nm (4.25 µm)
Carbonyl (C=O)	~1,700 cm⁻¹	5,882 nm (5.9 µm)
Fingerprint Region Start	1,500 cm⁻¹	6,666 nm (6.7 µm)
Silicon-Oxygen (Si-O)	~1,100 cm⁻¹	9,090 nm (9.1 µm)
Terahertz Gap Start	333 cm⁻¹	30,000 nm (30 µm)

Deep Dive Article What is Wavenumber? Understand why Spectroscopy prefers inverse centimeters and how it relates to energy.

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Why convert back to nanometers?

1. Detector Selection

You know your molecule absorbs at 2950 cm⁻¹, but photodetector datasheets specify ranges in microns (e.g., "InGaAs: 0.9 - 1.7 µm"). You must convert the wavenumber to wavelength (3.4 µm) to realize you need a PbSe detector, not InGaAs.

2. Diffraction Grating Math

The physics of diffraction gratings depends on the physical spacing of the grooves relative to the physical wavelength (nλ = d sin θ). You cannot calculate dispersion angles directly from wavenumbers.

3. Laser Tuning

Quantum Cascade Lasers (QCLs) are often sold by "center wavenumber," but the optical cavity length and coating thickness are designed in physical length (microns).

4. Atmospheric Windows

Transmission through the atmosphere is defined by "windows" (e.g., the 8-12 µm thermal window). Converting wavenumbers helps you see if your signal will be absorbed by water vapor or pass through clearly.

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