This calculator estimates full width at half maximum for measured peaks, Gaussian distributions, and Lorentzian line shapes. It also reports HWHM, equivalent sigma, half-maximum positions, Q factor, and a plotly graph.
FWHM Calculator Form
Example Data Table
| Case | Inputs | Computed FWHM | Useful Note |
|---|---|---|---|
| Measured Peak | xL = 4.2, xR = 7.8 | 3.6 units | Direct width between half-maximum crossings. |
| Gaussian Sigma | σ = 1.5 | 3.532230 units | FWHM = 2.35482σ |
| Gaussian Variance | Variance = 2.25 | 3.532230 units | σ = √variance first. |
| Lorentzian Peak | γ = 0.9 | 1.8 units | FWHM = 2γ |
Formula Used
1) Direct half-maximum width
FWHM = xR − xL
xL and xR are the left and right positions where the signal reaches half of its peak height above baseline.
2) Half-maximum level
Half Maximum = Baseline + (Peak − Baseline) / 2
This level is the amplitude used to find the left and right crossing positions in measured data.
3) Gaussian relation
FWHM = 2√(2ln2) · σ ≈ 2.35482σ
Use this when the distribution or line shape is well approximated by a Gaussian peak.
4) Variance relation
σ = √variance
FWHM = 2√(2ln2) · √variance
This mode is convenient when variance is known instead of standard deviation.
5) Lorentzian relation
FWHM = 2γ
Here γ is the half width at half maximum, also called HWHM, for a Lorentzian profile.
6) Quality factor
Q = Center / FWHM
A larger Q factor indicates a narrower peak relative to its center position.
How to Use This Calculator
- Select the method that matches your available data.
- Enter a unit label such as nm, Hz, eV, ms, or mm.
- Provide center, baseline, and peak values when relevant.
- For direct measurement, enter the left and right half-maximum positions.
- For Gaussian mode, enter sigma or variance.
- For Lorentzian mode, enter gamma, which equals HWHM.
- Click Calculate FWHM to show the result above the form.
- Review the graph, summary metrics, and use CSV or PDF export if needed.
Physics Notes
In spectra, FWHM describes how broad a line appears at half of its maximum height. In time-domain pulse work, it describes pulse duration measured at half amplitude. In resonance systems, width can be tied to damping, losses, and selectivity.
For real experimental data, fitting a model curve is often more reliable than reading two points manually from noisy samples. This page supports quick estimation and comparison, not full nonlinear fitting.
FAQs
1) What does FWHM mean?
FWHM stands for full width at half maximum. It measures the width of a peak between the two positions where the signal reaches half of its peak height above baseline.
2) When should I use Gaussian mode?
Use Gaussian mode when your signal shape is approximately bell-shaped and you know sigma or variance. This is common in beam profiles, instrumental broadening, and many statistical distributions.
3) What is gamma in the Lorentzian option?
Gamma is the half width at half maximum. For a Lorentzian peak, the full width at half maximum is exactly twice gamma.
4) Why does baseline matter?
Baseline shifts change the half-maximum amplitude level. If you ignore a nonzero baseline, the left and right crossing positions can be wrong, which changes the computed FWHM.
5) What is the Q factor shown in the result?
Q factor compares the center position to the peak width. A larger value means the peak is relatively narrow compared with its center, often indicating better selectivity or weaker damping.
6) Can I use wavelength, frequency, time, or distance units?
Yes. The calculator is unit-consistent, so you can use any position unit as long as all related inputs use the same unit system.
7) Does this calculator fit noisy experimental data automatically?
No. It calculates width from entered values and draws an illustrative curve. For noisy data, preprocess the signal or fit a Gaussian or Lorentzian model first.
8) What happens if I enter the right point before the left point?
That is fine. The calculator sorts the two half-maximum positions internally and uses their absolute difference, so the FWHM remains correct.