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FWHM Calculator

Calculate peak width from formulas or measured data, inspect half-maximum crossings, compare fitted models, analyse multiple peaks, and export clear scientific results with confidence.

Calculation setup

Crossing positions

Used for the baseline-corrected half level.

Gaussian standard deviation

Gaussian variance

Gaussian coefficient

Equation: y = A exp[−a(x−μ)²].

Lorentzian half-width

Voigt component widths

Resonance quality factor

Spectral resolving power

Instrument broadening correction

Measured peak data

Use comma, semicolon, tab, or spaces. A header row is allowed.

Detection and baseline

Fitting and correction

Formula used

Crossings: FWHM = x₂ − x₁
Gaussian: FWHM = 2√(2 ln 2)σ ≈ 2.35482σ
Gaussian coefficient: FWHM = 2√(ln 2 ÷ a)
Lorentzian: FWHM = 2γ
Voigt approximation: 0.5346L + √(0.2166L² + G²)
Quality factor: FWHM = f₀ ÷ Q
Resolving power: Δλ = λ ÷ R
Half level = baseline + (peak − baseline) ÷ 2

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

  1. Select the calculation mode matching your available measurements.
  2. Choose compatible input and output horizontal-axis units.
  3. Enter formula values or paste paired dataset values.
  4. Set baseline, smoothing, detection, and fitting options.
  5. Calculate, inspect warnings, and review the plotted crossings.
  6. 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.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.