Raman Shift Calculator

Convert between Raman shift (cm⁻¹) and Stokes or anti-Stokes wavelength for any laser, with the vibrational energy and the anti-Stokes/Stokes ratio.

Model: Exact

Laser wavelength λ_L (nm, vacuum)Raman shift Δν̃ (cm⁻¹)Measured line wavelength (nm, vacuum)Sample temperature (K)Chart from (cm⁻¹)Chart to (cm⁻¹)

Detector

Stokes line λ_S

561.893 nm

17796.99 cm⁻¹

Anti-Stokes line λ_aS

505.127 nm

19796.99 cm⁻¹

Laser wavenumber ν̃_L

18796.99 cm⁻¹

Vibrational energy hcΔν̃

123.984 meV

Frequency cΔν̃ = 29.979 THz

Anti-Stokes/Stokes ratio at 295 K

0.01049

Photon counts, m = 3

Shift of a line at 561.89 nm

999.9 cm⁻¹

Stokes side

All wavelengths are vacuum values. Spectrometers calibrated in air read about 0.15 nm shorter at 532 nm (n_air ≈ 1.00028), which moves a shift by under 1 cm⁻¹ when the laser and the line are read the same way.

Scattered wavelength vs Raman shift

Stokes
Anti-Stokes
Current shift

Common Raman bands at 532.0 nm

Band	Shift (cm⁻¹)	Stokes λ (nm)	Anti-Stokes λ (nm)
Silicon, optical phonon	520.7	547.16	517.66
Cyclohexane, ring breathing	801.3	555.69	510.25
Diamond, optical phonon	1332	572.57	496.80
Graphite, G band	≈ 1580	580.82	490.75
C=O stretch	≈ 1700	584.90	487.88
CH₂ symmetric stretch	≈ 2850	627.08	461.96
O–H stretch, liquid water (broad)	≈ 3400	649.48	450.51

Silicon, cyclohexane and diamond are shift-calibration standards; ≈ marks typical group frequencies, which move with the molecule and its surroundings. The graphite D band near 1350 cm⁻¹ moves with the laser wavelength.

ν̃_L = 10⁷/λ_L (cm⁻¹, λ in nm)

Stokes: ν̃_S = ν̃_L − Δν̃, λ_S = 10⁷/ν̃_S

Anti-Stokes: ν̃_aS = ν̃_L + Δν̃, λ_aS = 10⁷/ν̃_aS

I_aS/I_S = (ν̃_aS/ν̃_S)^m · exp(−hcΔν̃/k_BT), m = 3 (photons) or 4 (power)

The shift is the vibrational wavenumber of the molecule, so it does not depend on the laser; the scattered wavelengths do. The anti-Stokes line starts from the thermally populated excited level, which makes it weaker and the ratio a thermometer. The ratio assumes a harmonic vibration and equal cross-sections on both sides, which fails under resonance excitation.

Model and references

Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers

Exact conversions by energy conservation, in vacuum wavelengths. The anti-Stokes/Stokes ratio assumes a harmonic vibration in thermal equilibrium and equal Raman cross-sections on both sides (not under resonance excitation).

Long D. A. (2002). The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules. Wiley. Stokes and anti-Stokes intensities and their temperature dependence. doi:10.1002/0470845767
McCreery R. L. (2000). Raman Spectroscopy for Chemical Analysis. Wiley. Raman shift standards (silicon, cyclohexane, diamond). doi:10.1002/0471721646

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