A complete, step-by-step method for calculating the optical band gap from UV–Vis absorbance or transmittance data — the same workflow the calculator performs for you.
Calculating a band gap with a Tauc plot is a seven-step calculation: clean the spectrum, convert the axis to photon energy, obtain the absorption coefficient, choose the transition exponent, plot (αhν)ⁿ againsthν, fit the linear region, and read the intercept. Do that correctly and the number you extract is the optical band gap of the material in electronvolts.
You can do it by hand in a spreadsheet, but the Tauc plot calculatoron this site runs every step in the browser — including the automatic fit and the regression statistics — from a raw instrument file.
Start from a clean spectrum. If the absorbance does not approach zero below the absorption edge, subtract a baseline — a sloping background will tilt the Tauc curve and shift the intercept.
Apply the transmittance conversion only when your file contains transmittance. Absorbance files can be used directly.
The x-axis of a Tauc plot is photon energy, not wavelength. Convert nanometres to electronvolts with the relation:
If your instrument already exports energy or wavenumbers, convert those to eV instead and skip this step.
The Tauc relation is written for the absorption coefficient α. For a film of thicknessd in centimetres, Beer–Lambert gives:
When the thickness is unknown — suspensions, powders, uncalibrated films — use the absorbance proxy (Ahν)ⁿ. Because the intercept is invariant under a vertical scale factor, the extracted Eg is usually unaffected, provided you stay consistent between samples.
The exponent encodes the electronic transition you are probing:
| Transition | n | Typical materials |
|---|---|---|
| Direct allowed | 2 | ZnO, GaAs, CdTe, MAPbI₃ |
| Indirect allowed | 1/2 | Si, Ge, anatase TiO₂, GaP |
| Direct forbidden | 3/2 | Cu₂O, SnO |
| Indirect forbidden | 2/3 | SnO₂, rare-earth oxides |
Choose the model from the physics of the material — not from which exponent produces the straightest line. See direct vs indirect band gapfor a fuller comparison.
With x = hν andy = (αhν)ⁿ, draw the scatter plot. You should see a low-signal region below the gap, a steep rising edge, and a flattening at high energy where the detector saturates. The steep edge is the part you will fit.
Fit y = mx + b by least squares over the straight onset, then set y = 0:
In the calculator this fit is interactive — drag the window and the intercept updates live. If you are working manually, record the point range you used so the analysis is reproducible.
The exponential sub-bandgap region is not linear in the Tauc sense and drags the intercept down.
Plotting transmittance directly inverts the edge and produces a meaningless fit.
Using n = 2 on an indirect material (or vice versa) changes the curve shape and biases Eg.
Above A ≈ 2–2.5 the detector flattens; including that plateau destroys linearity.
Convert the wavelength axis to photon energy, convert transmittance to absorbance if needed, apply the correct Tauc exponent, plot (αhν)ⁿ against hν, fit the linear onset and read the x-axis intercept as the optical band gap.
Multiply absorbance by photon energy, raise the product to the exponent n for your transition, then fit and extrapolate the linear region. If the sample thickness is known, convert A to α first for a quantitative absorption coefficient.
First convert transmittance to absorbance: T = %T/100, then A = −log10(T). After that the workflow is identical to absorbance data — plot (αhν)ⁿ vs hν and extrapolate the linear region.
The steepest straight segment at the absorption edge. Exclude the exponential Urbach tail underneath it and the flattening caused by detector saturation above it.
Upload a TXT, CSV or DAT export and the calculator performs all seven steps — including the fit — in seconds.