Formula used
Each formula uses a consistent horizontal-axis unit. Dataset mode interpolates crossing positions between neighbouring samples. Always review assumptions before reporting final scientific measurements.
How to use this calculator
- Select the calculation mode matching your available measurements.
- Choose compatible input and output horizontal-axis units.
- Enter formula values or paste paired dataset values.
- Set baseline, smoothing, detection, and fitting options.
- Calculate, inspect warnings, and review the plotted crossings.
- Copy results, download CSV, or print a PDF report.
Example data
| Application | Available values | Suggested mode | Example result |
|---|---|---|---|
| Gaussian signal | σ = 2 ms | Gaussian standard deviation | 4.70964 ms |
| Lorentzian line | γ = 0.8 nm | Lorentzian HWHM | 1.6 nm |
| Resonator | f₀ = 10 MHz, Q = 200 | Quality factor | 50 kHz |
| Spectrometer | λ = 600 nm, R = 3000 | Resolving power | 0.2 nm |
| Experimental profile | Paired x and y values | Measured dataset | Interpolated automatically |
Interpretation and limitations
FWHM describes width at half the baseline-corrected peak amplitude. It does not fully describe asymmetry or long tails. Compare fitted residuals before selecting a peak model.
Smoothing can suppress noise and alter narrow features. Excessive windows may broaden or merge neighbouring peaks. Test several settings before accepting automated peak widths.
Instrument correction assumes matching Gaussian or Lorentzian profiles. Mixed profiles require more complete deconvolution methods. Treat corrected widths carefully near the instrument resolution.
Frequently asked questions
What does FWHM measure?
It measures a peak’s width at half amplitude. The baseline is included when calculating half height. Narrower widths usually indicate sharper or better-resolved peaks.
How is baseline-corrected half height calculated?
Subtract the baseline from the peak maximum first. Divide that amplitude by two, then restore baseline. This avoids errors from offset or background signals.
Can the calculator analyse negative peaks?
Yes, select the negative peak direction option. The detector then measures downward amplitude from baseline. Crossing interpolation works the same way afterward.
Does dataset mode support irregular spacing?
Yes, x values may use irregular intervals. Linear interpolation estimates each half-height crossing. Dense sampling generally produces more stable width estimates.
Which baseline method should I select?
Use edge averaging when peak-free edges exist. Use manual baseline for known background levels. Compare alternatives when the background slopes or drifts.
What does the smoothing window do?
It applies a centred moving average before detection. Small windows reduce noise without severe distortion. Large windows can broaden and merge close peaks.
How are multiple peaks detected?
Local maxima must exceed the chosen amplitude threshold. Minimum separation removes nearby duplicate candidates. Select all peaks to create batch results.
Are Gaussian and Lorentzian fits nonlinear optimisations?
No, dataset fits use measured centre, amplitude, and FWHM. They provide quick profile comparisons and residual statistics. Dedicated fitting software may refine every parameter.
When is instrument correction appropriate?
Use it when instrument broadening is independently known. Choose the profile matching both measured contributions. Invalid assumptions can produce misleading intrinsic widths.