Tafel slope and exchange current density calculator

Classical Tafel analysis plots $\log |j|$ against the overpotential $\eta$, the electrode potential measured from the reaction’s equilibrium potential, finds a linear region, and takes the kinetic parameters from the slope and intercept of that region (Taffit, ACS Meas Sci Au 2025, doi:10.1021/acsmeasuresciau.5c00038). The calculator fits

$$\eta =a+b\cdot {\log }_{10}|j|$$

by least squares over the $|\eta |$ range you choose. $b$ is the Tafel slope, reported in mV per decade (lower slopes mean that a decade more current costs less overpotential). Setting $\eta =0$ gives the exchange current density, ${\log }_{10}{j}_0=-a/b$, the current at which the forward and backward reactions are equal at equilibrium. $j_0$ comes out in the unit of your current column.

The slope relates to the transfer coefficient through $b=\ln 10\cdot RT/(\alpha \cdot n\cdot F)$, 59.16 mV/dec for $\alpha \cdot n=1$ at 298.16 K; the calculator reports the apparent $\alpha \cdot n=\ln 10\cdot RT/(F\cdot |b|)$ at the temperature you enter ($R=8.314\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$, $F=96485\mathrm{C}{\mathrm{mol}}^{-1}$, doi:10.1021/acsaem.5c01865). Treat it as apparent: $n$ is not always 1 (it is two for the HER on Pt, as the Taffit paper notes).

Limits of the method. The linear Tafel form holds only where $|\eta |$ is large enough that one direction of the reaction carries the current, and below the overpotentials where mass transport starts to limit it; it cannot be applied around $\eta \to 0$. There is no single agreed rule for choosing the region, and different valid ranges can give different slopes and j₀ (Taffit). So use iR-corrected data from a slow scan, fit only the straight part, and report the range. Exchange current densities in the literature are likewise found by extrapolating the Tafel line to the reversible potential (doi:10.1177/1478422X241227829).

To put an LSV on the RHE scale and iR-correct it first, use the RHE converter.

The built-in example is an illustrative OER curve, not a measured one: nine points from 1.45 to 1.61 V vs RHE with current densities from 0.42 to 32 mA cm⁻². With the OER equilibrium at 1.23 V, the overpotentials run from 220 to 380 mV.

Fitting every point gives 83.1 mV/dec with R² = 0.979, a sign that the curve is not one straight line. Restricting the fit to $|\eta |=260\text{–}320\mathrm{mV}$ (4 points) gives a Tafel slope of 79.4 mV/dec, R² = 0.998, intercept $a=236.9\mathrm{mV}$, and an exchange current density of $\mathbf{1.04}\times {\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{mA}{\mathbf{cm}}^{\mathbf{-}\mathbf{2}}$ (${\log }_{10}{j}_0=-2.98$). The apparent $\alpha \cdot n$ is 0.745 at 25 °C.