Is the foil thin, or is it thicc? One logarithm settles it.
Point EELS at your specimen for two seconds and the low-loss spectrum already contains its thickness: t/λ = ln(It/I0), the log-ratio method. This tool runs that analysis on your own spectrum, entirely in your browser (nothing is uploaded anywhere), and converts t/λ to nanometers using two published mean-free-path models so you can see the systematic spread instead of trusting one number. New to the spectrum itself? Start with the companion guide, How to read an EELS spectrum.
Use a built-in demo to see the workflow, or load your own export: two-column text (energy in eV, counts; comma, semicolon, tab, or space separated) or EMSA/MAS .msa, the plain-text exchange format every vendor package can write. One-column count lists work too; the tool will ask for the dispersion. The spectrum should cover the zero-loss peak through at least ~50–100 eV.
No spectrum loaded yet. Try a demo button above.
Drag the dashed divider on the plot (or use the slider) to move the zero-loss window. A good split sits in the valley between the zero-loss peak and the first plasmon; on a decent spectrum, t/λ barely moves as you nudge it.
Integrate I0 and It in your acquisition software (Gatan DM's Thickness tool reports both), then type them here.
Converting t/λ to nanometers needs λ, and λ depends on beam energy, on how much of the scattering your collection aperture actually caught (β, and in STEM also the convergence α), and on the material. The two models below want slightly different material inputs: Malis wants an effective atomic number, Iakoubovskii wants a density. Pick a preset and both are filled; edit anything.
Inelastic scattering events are independent, so the number each electron suffers follows Poisson statistics. The unscattered fraction is then I0/It = e−t/λ, and one logarithm turns the measured ratio into thickness in units of the inelastic mean free path λ. That part is nearly assumption-free, which is why t/λ is the number worth quoting in your methods section. All the modelling risk lives in converting λ to nanometers, so this tool shows two independent parameterizations side by side: Malis et al. (1988), built on an effective atomic number, and Iakoubovskii et al. (2008), fitted to measurements on 24 materials using density, with explicit convergence- and collection-angle dependence. When α > 0, the Malis number uses Egerton's effective collection angle β* in place of β. The two are not supposed to be averaged into one comfortable number: benchmark measurements on silicon found the Iakoubovskii model accurate at large collection angles while Malis underestimates λ by 15% or more, which is exactly why this tool refuses to show you just one answer.
Log-ratio: t/λ = ln(It/I0), with I0 the zero-loss integral and It the whole recorded spectrum.
Malis: λ = 106 F E0 / (Em ln(2βE0/Em)) nm, with E0 in keV, β in mrad, mean energy loss Em = 7.6 Zeff0.36 eV, relativistic factor F = (1 + E0/1022)/(1 + E0/511)², and for compounds Zeff = ΣfiZi1.3 / ΣfiZi0.3 over atomic fractions fi. Stated accuracy about ±10–20%, for β up to roughly 20–25 mrad.
Iakoubovskii: 1/λ = (11 ρ0.3)/(200 F E0) · ln(A θC² / (B θE²)) with A = α²+β²+2θE²+|α²−β²|, B = α²+β²+2θC²+|α²−β²|, characteristic angle θE = 5.5 ρ0.3/(F E0) mrad, and an empirical saturation angle θC = 20 mrad (scattering beyond it contributes little, so huge apertures stop helping). Same F; ρ in g/cm³; angles in mrad. Implemented exactly as in the paper's Eq. 9, matching the reference implementation in the open-source eXSpy/HyperSpy package.
Effective angle for Malis when α > 0: Egerton's β* algorithm (from the book's appendix), evaluated at E = Em: convergence blurs which scattering angles the aperture accepts, and β* is the equivalent parallel-beam aperture. When α = 0, β* = β exactly.
Either, knowingly, but Iakoubovskii is the better-supported default. Malis (1988) needs only composition (Zeff), is built into most acquisition software, and behaves sensibly for β up to ~20 mrad; but direct λ measurements on silicon found it at least 15% short, and against Iakoubovskii it runs 20–40% lower at typical TEM collection angles. Iakoubovskii (2008) was fitted to measurements on two dozen materials at 200 kV, needs the density, and treats convergence and collection angles explicitly, which suits STEM geometries. Two habits keep you honest either way: quote which model (plus β and E0) produced any nanometer value, and remember that t/λ itself is model-free, so relative statements ("twice as thick," "thinnest here") survive any future revision of λ.
Partly systematics (the λ parameterizations themselves disagree by 15–40%, see the model question above), but often the disagreement is physical: CBED's Kossel–Möllenstedt analysis measures the crystalline thickness that diffracts, while EELS measures everything the beam crossed, including amorphous FIB damage, native oxide, and contamination on both surfaces. On a FIB lamella those layers can be tens of nanometers combined, so EELS reading 15–25% above CBED is common and meaningful rather than an error. Measuring both is exactly how damage-layer thickness gets estimated; this site's CBED Thickness Tool handles the diffraction side of that comparison.
Aim for t/λ < 0.3–0.5 at the analysis position: beyond that, plural scattering redistributes intensity into the region above each edge and background subtraction gets ugly. Since λ is roughly 100–200 nm for most inorganic materials at 200 kV (depending on material, model, and collection angle), that means foils in the few-tens-of-nanometers range. Mapping t/λ first, then quantifying only where the map is green, is the workflow that saves the afternoon.
Less than you would fear, on a good spectrum. The valley between the zero-loss peak and the first plasmon is deep for materials with Ep above ~10 eV, so t/λ plateaus while the divider is anywhere in it (nudge the slider and watch). It matters more for narrow-gap or organic materials whose loss function starts at a few eV, and for very thick specimens where the valley fills in; there, quote the window you used. The fancier alternative (fitting and deconvolving the ZLP shape) buys precision mainly when the peak and losses genuinely overlap.
Two-column text (energy eV, counts) with comma, semicolon, tab, or space separators; EMSA/MAS .msa in Y or XY mode; or a bare one-column count list plus the dispersion you type in. Everything runs in JavaScript in your browser tab: no upload, no server, and the page works offline once loaded. If your software only writes .dm4, export the spectrum as text first (in DigitalMicrograph: File → Save As → Text, or right-click the spectrum).
T. Malis, S. C. Cheng, R. F. Egerton, "EELS log-ratio technique for specimen-thickness measurement in the TEM," J. Electron Microsc. Tech. 8, 193–200 (1988). K. Iakoubovskii, K. Mitsuishi, Y. Nakayama, K. Furuya, "Thickness measurements with electron energy loss spectroscopy," Microsc. Res. Tech. 71, 626–631 (2008). P. L. Potapov, "The experimental electron mean-free-path in Si under typical (S)TEM conditions," Ultramicroscopy (2014): the Si benchmark quoted above (150 nm at 200 kV, 179 nm at 300 kV, Iakoubovskii accurate, Malis at least 15% short). R. F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope, 3rd ed., Springer (2011), including the effective-aperture algorithm. Cross-checked numerically against the open-source eXSpy (HyperSpy) implementation of the same formulas. Background reading: the plural-scattering pages of the Gatan EELS Atlas site (eels.info).
@misc{tripathy2026eelsthicknesscalculator,
author = {Tripathy, Manisha},
title = {EELS Thickness Calculator},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/eels-thickness-calculator}},
note = {Interactive analysis tool}
}