# Tauc plot band gap calculator (UV–vis)

> Band gap from a UV–vis absorbance spectrum with a Tauc plot: direct or indirect transition, straight-line fit and intercept, chart and CSV. Free.

URL: https://www.labcanvas.com/tools/tauc-plot-band-gap-calculator

Convert each wavelength to photon energy (E = 1240/λ, E in eV, λ in nm), plot (αhν)² against hν for a direct allowed transition or (αhν)^½ for an indirect one, fit a straight line to the steep part of the absorption edge and extend it to the energy axis: the intercept is the optical band gap Eg. Paste your spectrum and the calculator does the plot, the fit and the intercept.

## Quick answer

- **What it does:** Finds the optical band gap from a UV–vis absorbance spectrum with a Tauc plot, for direct or indirect transitions, by a straight-line fit and its energy-axis intercept.
- **Formula:** E (eV) = 1240 ÷ λ (nm); plot (αhν)^(1/n) against hν, n = ½ direct, n = 2 indirect; Eg = intercept of the linear fit with the energy axis.
- **Example:** For the built-in synthetic direct-gap spectrum, (αhν)² fitted from 3.196 to 3.388 eV meets the axis at Eg = 3.19 eV, and 3.20 eV after subtracting a 0.02 baseline.

Free, in the browser, no account needed. Updated 2026-11-08.

## Features

- Paste absorbance against wavelength (nm) or photon energy (eV), straight from a spectrometer export or a spreadsheet
- Direct allowed (\(n = \tfrac{1}{2}\), \((\alpha h\nu)^2\)) or indirect allowed (\(n = 2\), \((\alpha h\nu)^{1/2}\)) transitions
- Suggested linear region (the steepest straight stretch of the edge) that you can change by typing the energy range
- Band gap from the straight-line intercept, with the points used, R² and the matching absorption-edge wavelength
- Optional baseline subtraction for the flat absorbance below the gap
- Optional film thickness to plot \(\alpha\) in cm⁻¹ (the band gap does not change)
- Tauc plot with the fitted points and line as PNG or SVG, results and plotted data as CSV; nothing is uploaded

## How to use it

1. **Paste the spectrum**: Two columns: wavelength in nm (or photon energy in eV) and absorbance. A header row is skipped.
2. **Choose the transition**: Direct allowed (\(n = \tfrac{1}{2}\)) plots \((\alpha h\nu)^2\); indirect allowed (\(n = 2\)) plots \((\alpha h\nu)^{1/2}\). Use what is known for your material.
3. **Remove the baseline**: If the absorbance is not zero below the gap, enter that flat level so it is subtracted before the plot.
4. **Check the linear region**: Look at the plot: the suggestion is the steepest straight part of the edge. Type a different range in eV if it is not the part you mean.
5. **Read and export**: Read \(E_\mathrm{g}\) where the line meets the energy axis, and download the plot (PNG or SVG) and the data (CSV). Report the range you fitted.

## At a glance

| | |
| --- | --- |
| Method | Tauc plot: \((\alpha h\nu)^{1/n}\) against \(h\nu\), straight-line fit, intercept on the energy axis |
| Transitions | Direct allowed (\(n = \tfrac{1}{2}\)) and indirect allowed (\(n = 2\)) |
| Photon energy | \(E = 1240 / \lambda\) (eV, nm) |
| Input | Absorbance against wavelength (nm) or energy (eV); optional baseline and film thickness |
| Linear region | Suggested automatically, editable |
| Export | Tauc plot as PNG or SVG; data and result as CSV |

## How it works

$$E\ (\mathrm{eV}) = \frac{1240}{\lambda\ (\mathrm{nm})}$$

$$\alpha h\nu \propto (h\nu - E_\mathrm{g})^n$$

$$(\alpha h\nu)^{1/n} = A \cdot (h\nu - E_\mathrm{g})$$

**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: \(n = \tfrac{1}{2}\) 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](https://doi.org/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](https://doi.org/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](https://doi.org/10.1021/acs.jpclett.3c01416). Rai R, Kaleem M, Bhandari R, Misra A. *ChemPlusChem* 2025;90:e202400660, [doi:10.1002/cplu.202400660](https://doi.org/10.1002/cplu.202400660) (\(E = 1240/\lambda\)).

## Worked example: a synthetic direct-gap spectrum

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.

- Each wavelength becomes an energy: 400 nm is \(1240/400 = 3.10\ \mathrm{eV}\).
- With the direct transition chosen, \((A \cdot h\nu)^2\) is plotted against \(h\nu\).
- The suggested range runs from 3.196 to 3.388 eV (12 points, R² = 0.9995) and its line meets the axis at \(E_\mathrm{g} = \mathbf{3.19\ eV}\), an absorption edge near 389 nm.
- 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.

## Questions

### How do I calculate the band gap from a UV–vis spectrum?

Convert wavelength to photon energy with \(E = 1240/\lambda\) (eV, nm), plot \((\alpha h\nu)^2\) against \(h\nu\) for a direct transition or \((\alpha h\nu)^{1/2}\) for an indirect one, fit a straight line to the steep linear part of the absorption edge and extend it to the energy axis. The intercept is the optical band gap.

### Should I use \((\alpha h\nu)^2\) or \((\alpha h\nu)^{1/2}\)?

It depends on the transition. The Tauc exponent \(n\) is ½ for a direct band gap and 2 for an indirect one, and the plot is \((\alpha h\nu)^{1/n}\): \((\alpha h\nu)^2\) for direct, \((\alpha h\nu)^{1/2}\) for indirect. Idriss (2026) gives rutile TiO₂ (direct) and anatase TiO₂ (indirect) as examples.

### Can I use absorbance instead of the absorption coefficient?

Yes. Scaling \(\alpha\) by a constant does not move the point where the fitted line meets the energy axis, so absorbance of the same sample gives the same band gap. Enter the film thickness only if you want \(\alpha\) in cm⁻¹ on the axis.

### Which part of the curve should I fit?

The steep, straight part of the edge just above the onset, not the tail below it or the bend at the top. The calculator suggests the steepest straight stretch; check it on the plot and report the energy range you used.

### Why is my Tauc band gap lower than the literature value?

A sub-gap absorption tail (Urbach tail), excitonic absorption and a non-zero baseline all pull the intercept down; Garg et al. (2023) found Tauc estimates below the accurately known gaps of two niobates. Subtract the baseline below the gap (Zhong et al. 2023) and fit only the steep part of the edge.

### Can I use diffuse reflectance data?

Yes, after converting reflectance with the Kubelka–Munk function in your spectrometer software: \(F(R)\) is approximately proportional to the absorption coefficient and is analysed the same way (Garg et al. 2023). Paste \(F(R)\) in place of absorbance.

### Does the Tauc plot work for a mixture of phases?

Not reliably. A mixed-phase sample, such as anatase and rutile TiO₂ together, has two kinds of transition, and one Tauc exponent cannot describe both (Idriss 2026).