Tauc plot band gap calculator (UV–vis)

$$E(\mathrm{eV})=\frac{1240}{\lambda (\mathrm{nm})}$$$$\alpha h\nu \propto (h\nu -E_{\mathrm{g}}{)}^n$$$$(\alpha h\nu {)}^{1/n}=A\cdot (h\nu -E_{\mathrm{g}})$$

Tauc plot. Tauc analysis of a UV–vis absorption spectrum is the routine way to estimate the optical band gap, and it needs the Tauc exponent $n$ of the electronic transition: $n=\frac{1}{2}$ for a direct band gap and $n=2$ for an indirect one (Idriss 2026, who uses rutile and anatase TiO₂ as the two cases). With $\alpha h\nu \propto (h\nu -E_{\mathrm{g}}{)}^n$, the quantity $(\alpha h\nu {)}^{1/n}$ is a straight line in $h\nu$ just above the gap, so $(\alpha h\nu {)}^2$ is plotted for a direct and $(\alpha h\nu {)}^{1/2}$ for an indirect transition. A least-squares line is fitted to the linear part of the edge and extended to zero; where it meets the energy axis is $E_{\mathrm{g}}$ (Garg et al. 2023).

Absorbance or α. Multiplying $\alpha$ by a constant does not move the point where the line meets the axis, so absorbance (proportional to α for a fixed sample) can be used as it is. With a film thickness $d$, the tool plots $\alpha =\ln 10\cdot A/d$, from $A={\log }_{10}(I_0/I)$ and $I=I_0\cdot e^{-\alpha d}$ with reflection ignored. Photon energies come from $E=1240/\lambda$ (Rai et al. 2025).

Baseline and limits. Absorption below the gap makes different extrapolations disagree; removing the baseline before building the plot resolves it (Zhong et al. 2023). A Tauc estimate also tends to fall below the true gap when the spectrum has a sub-gap (Urbach) tail or excitonic absorption, and depends on sample thickness (Garg et al. 2023). It can mislead for mixed-phase samples with two kinds of transition (Idriss 2026). The linear region is suggested by a simple rule, the steepest window of consecutive points whose straight-line fit has $R^2\ge 0.99$; it is a starting point, not a rule from the literature.

Sources: Idriss H. Extraction of band gap energies and composition of mixed-phase polycrystalline semiconductors; a possible alternative method. J Phys Condens Matter 2026;38, doi:10.1088/1361-648X/ae3cf5. Garg AB, Vie D, Rodriguez-Hernandez P, Muñoz A, Segura A, Errandonea D. Accurate determination of the bandgap energy of the rare-earth niobate series. J Phys Chem Lett 2023;14:1762–1768, doi:10.1021/acs.jpclett.3c00020. Zhong H et al. Idealizing Tauc plot for accurate bandgap determination of semiconductor with ultraviolet-visible spectroscopy. J Phys Chem Lett 2023;14:6702–6708, doi:10.1021/acs.jpclett.3c01416. Rai R, Kaleem M, Bhandari R, Misra A. ChemPlusChem 2025;90:e202400660, doi:10.1002/cplu.202400660 ($E=1240/\lambda$).

The built-in example is a synthetic spectrum, not a measurement: absorbance from 300 to 500 nm in 2 nm steps, generated for a direct allowed gap at 3.20 eV with a weak absorption tail below the gap and a flat absorbance of 0.02 underneath.

1. Each wavelength becomes an energy: 400 nm is $1240/400=3.10\mathrm{eV}$.
2. With the direct transition chosen, $(A\cdot h\nu {)}^2$ is plotted against $h\nu$.
3. The suggested range runs from 3.196 to 3.388 eV (12 points, R² = 0.9995) and its line meets the axis at $E_{\mathrm{g}}=\mathbf{3.19}\mathbf{eV}$, an absorption edge near 389 nm.
4. Entering 0.02 as the baseline and fitting again gives 3.20 eV, the gap the spectrum was made with: the flat absorbance under the edge had pulled the intercept down.