Calculator
Example data table
| Excitation λ₀ (nm) | Scattered λs (nm) | Raman shift (cm⁻¹) | Frequency shift (THz) | Energy shift (meV) |
|---|---|---|---|---|
| 532 | 550 | 615.034 | 18.440 | 76.262 |
| 633 | 670 | 871.631 | 26.141 | 108.098 |
| 785 | 820 | 546.150 | 16.367 | 67.689 |
Values are illustrative; instrument calibration and refractive index corrections can change reported shifts.
Formula used
- Wavenumber from wavelength: σ (cm⁻¹) = 10⁷ / λ (nm)
- Raman shift: Δσ (cm⁻¹) = σ₀ − σs = (10⁷/λ₀) − (10⁷/λs)
- Scattered wavelength from shift: 1/λs = 1/λ₀ − Δσ/10⁷
- Frequency shift: Δf (Hz) = c · Δσ (m⁻¹), with Δσ (m⁻¹) = 100 · Δσ (cm⁻¹)
- Energy shift: ΔE (J) = h · c · Δσ (m⁻¹); convert to eV by dividing by e
How to use this calculator
- Select a mode based on what your spectrometer reports.
- Enter the excitation wavelength of your laser in nanometers.
- Either enter the measured scattered wavelength or the Raman shift.
- Use a negative shift if your line is anti-Stokes.
- Press Calculate to view shift, frequency, and energy results.
- Use the export buttons to download the latest result.
Notes for advanced work
- Raman shifts are commonly reported in cm⁻¹ for easy comparison across lasers.
- Large shifts can approach a singularity; verify sign and magnitude.
- For higher accuracy, consider vacuum wavelength and index corrections.
Accurate Raman shifts improve peak assignment and material identification.
Professional article
1) Raman shift in spectroscopy
Raman spectroscopy reports vibrational and rotational information as a shift from the excitation line, not as an absolute wavelength. This shift-based reporting lets you compare spectra collected with different lasers. The calculator converts common inputs into Raman shift and also provides frequency and energy equivalents.
2) What the calculator computes
With excitation and scattered wavelengths, the tool converts each wavelength to wavenumber and subtracts them to obtain the Raman shift in cm⁻¹. In the alternate mode, you enter an excitation wavelength and a shift to compute the implied scattered wavelength. Both modes report sign and derived quantities.
3) Core units and conversions
Wavenumber is widely used because it is convenient for molecular spectra. Using λ in nanometers, σ = 10⁷/λ in cm⁻¹. A 1000 cm⁻¹ shift equals 1.0×10⁵ m⁻¹, and the frequency shift follows Δf = c·Δσ.
4) Stokes and anti-Stokes lines
Stokes scattering usually produces a longer scattered wavelength than the laser, giving a positive shift under the σ₀ − σs convention. Anti-Stokes lines can yield negative shifts when the sample is thermally excited. The calculator labels the interpretation to help validate your sign quickly.
5) Typical numeric ranges
Many fingerprint features fall roughly between 100 and 1800 cm⁻¹, while stretching modes may extend above 3000 cm⁻¹. A 500 cm⁻¹ shift corresponds to about 15.0 THz and roughly 62 meV. Energy output helps relate peaks to thermal scales.
6) Practical measurement workflow
Enter your laser wavelength, then input a peak as scattered wavelength or Raman shift depending on your software. Choose decimals that match your reporting needs. The results table includes wavenumbers, shift, frequency, and energy, making it easy to copy into lab notes or reports. For batches of peaks, repeat the calculation and export each run for consistent documentation.
7) Accuracy and calibration
High-precision work may require calibration with a standard such as silicon near 520.7 cm⁻¹, plus consistent assumptions about air versus vacuum wavelength. Detector mapping and peak fitting can add small offsets. The calculator applies ideal conversions, so report uncertainty separately. If you work at high resolution, keep more decimals during computation and round only at the final reporting stage.
8) Exporting for collaboration
The calculator stores the latest result and exports it as CSV or a simple PDF. Including excitation wavelength, scattered wavelength or shift, and derived values helps collaborators reproduce calculations. Consistent units and sign conventions reduce confusion when comparing datasets.
FAQs
1) Why is Raman shift reported in cm⁻¹?
cm⁻¹ scales linearly with inverse wavelength and is convenient for comparing spectra collected with different lasers. Peaks align by shift, not by absolute wavelength, which simplifies identification and database matching.
2) What does a negative Raman shift mean?
A negative value typically indicates an anti-Stokes line under the σ₀ − σs convention. It can occur when molecules are thermally populated in an excited state, so scattered photons gain energy.
3) Can I compute scattered wavelength from a target shift?
Yes. Select the mode that uses excitation wavelength and Raman shift. The calculator solves for the scattered wavelength implied by the chosen shift and reports all derived quantities for verification.
4) How do I compare Raman shift to energy?
The calculator converts Δσ to energy using ΔE = h·c·Δσ. It reports values in meV and eV, which helps relate vibrational features to thermal energy scales and other spectroscopy units.
5) Which laser wavelengths are common in practice?
Popular excitation lines include 488 nm, 514.5 nm, 532 nm, 633 nm, and 785 nm. Your instrument documentation will specify the exact wavelength, which you should enter for accurate conversions.
6) Why might my software show a slightly different shift?
Differences can arise from calibration, vacuum versus air wavelength assumptions, refractive index corrections, rounding, and peak fitting. Use standards and consistent settings when comparing instruments or publications.
7) What happens if the computed scattered wavelength looks unrealistic?
Very large shifts or an incorrect sign can drive the scattered wavelength toward an invalid value. Recheck the units, confirm the sign convention, and ensure the excitation wavelength matches your actual laser line.