Wavenumber to wavelength converter
Enter a wavenumber to find the corresponding wavelength.
Standard formula: λ (nm) = 107 / Wavenumber (cm⁻¹).
Enter a value to calculate.
How it works?
Converting Wavenumber to Wavelength
Wavenumber (\(\tilde{\nu}\)) is the inverse of wavelength (\(\lambda\)). It represents how many wave cycles fit into a standard distance (usually 1 centimeter).
Where:
- \(\lambda\) : Wavelength (in Nanometers).
- \(\tilde{\nu}\) : Wavenumber (in Inverse Centimeters).
- 10^7 : Conversion factor (nm per cm).
Example: A wavenumber of 20,000 cm⁻¹ corresponds to 500 nm (Green light).
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) |
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 (\(n\lambda = d \sin \theta\)). 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.
Related Engineering Tools
Convert Wavelength to Frequency (THz). Frequency is the "time-based" cousin of Wavenumber.
Photon EnergyCalculate the exact energy (eV or Joules) carried by a specific wavenumber.
Angstrom to NanometerSwitch between length scales when dealing with crystallography and atomic bonds.