Formula used
How to use this calculator
- Select a mode matching your peak shape or choose data mode.
- Enter parameters (σ, γ, or component values) as needed.
- For data mode, paste x and y pairs spanning the peak.
- Set a baseline if your signal has an offset.
- Click Calculate to display results above the form.
- Use Download CSV or Download PDF for reporting.
Example data table
Sample symmetric peak data with a clear half-maximum width.
| Point | x | y |
|---|---|---|
| 1 | -2.0 | 0.10 |
| 2 | -1.0 | 0.50 |
| 3 | 0.0 | 1.00 |
| 4 | 1.0 | 0.50 |
| 5 | 2.0 | 0.10 |
FWHM calculator: practical guide
1) What FWHM measures
Full width at half maximum (FWHM) is the peak width measured at 50% of the peak height above a baseline. It is widely used to describe spectral line broadening, laser linewidth, diffraction‑limited spot size proxies, pulse durations, and resolution in imaging and detectors. Compared with measuring the entire curve, FWHM is robust and easy to reproduce across experiments. It also integrates cleanly with automated peak fitting and quality control pipelines.
2) Gaussian peaks and sigma
Many random processes produce approximately Gaussian peaks. For an ideal Gaussian, the relationship between standard deviation and width is fixed: FWHM = 2·sqrt(2·ln 2)·σ. The factor equals about 2.35482, so a peak with σ = 0.85 has FWHM ≈ 2.0016. This conversion is useful when instrument response or thermal broadening is modeled using σ.
3) Lorentzian peaks and gamma
Lorentzian peaks are common in lifetime‑broadened spectroscopy and resonance phenomena. They are parameterized by the half‑width at half‑maximum (HWHM), denoted γ. The conversion is direct: FWHM = 2·γ. Because the Lorentzian has heavier tails than a Gaussian, two peaks with the same FWHM may still differ substantially in integrated area and baseline sensitivity.
4) Voigt profiles in real instruments
Real measurements often combine Gaussian and Lorentzian broadening, producing a Voigt profile. This calculator uses the Olivero–Longbothum approximation to estimate Voigt FWHM from the component widths. It is fast, accurate for many practical cases, and helps compare changes in broadening mechanisms without numerical convolution.
5) Computing FWHM from sampled data
When you only have measured (x,y) points, the calculator subtracts an optional baseline, finds the maximum, then locates the two half‑maximum crossings. Crossings are estimated using linear interpolation between neighboring samples, which is reliable when sampling is reasonably dense near the half‑maximum level.
6) Units, resolution, and uncertainty
FWHM inherits the units of your x‑axis: nanometers for wavelength, seconds for pulse timing, millimeters for position, or hertz for frequency. For discrete data, widen the scan range so both half‑maximum points are captured. If noise causes multiple crossings, smooth the data lightly or improve baseline selection to stabilize the half‑maximum level.
7) Reporting results for reproducibility
For clear reporting, record the chosen model (Gaussian, Lorentzian, Voigt, or data method), baseline value, and the computed peak position. This page can export a compact results table to CSV for lab notebooks and a PDF summary for attachments, ensuring consistent documentation across runs and collaborators.
FAQs
1) What does FWHM tell me physically?
FWHM summarizes how spread out a peak is at half height. It is often interpreted as resolution, linewidth, pulse width, or spatial blur, depending on what your x‑axis represents.
2) Should I use Gaussian or Lorentzian mode?
Use Gaussian when broadening comes from many small random effects. Use Lorentzian for resonance or lifetime broadening. If both mechanisms matter, use the Voigt approximation.
3) Why does baseline matter in data mode?
Half‑maximum is computed relative to the baseline‑corrected peak height. If the baseline is offset, the half‑maximum level shifts and the crossings move, changing the reported width.
4) My data never crosses half maximum on one side. What now?
Extend your measurement range or include more points on the missing side. You need two crossings around the peak for a valid FWHM estimate.
5) How accurate is linear interpolation for crossings?
It is usually accurate when sampling is dense near half maximum and noise is moderate. For coarse sampling, take more points or apply light smoothing before computing.
6) Can I compare FWHM values across experiments?
Yes, if you keep units, baseline method, and peak model consistent. Also note instrument settings, scan step, and any smoothing so comparisons remain meaningful.
7) What should I include when exporting results?
Include the mode, input parameters, baseline, peak position, and formula. The exported CSV/PDF from this page captures these fields for quick, consistent documentation.