Tafel slope and exchange current density calculator
A Tafel slope is found by plotting the overpotential η against log10 of the current density and fitting a straight line, η = a + b·log10|j|, over the linear part: b is the Tafel slope in mV per decade, and where the line reaches η = 0 it gives the exchange current density, log10 j₀ = −a/b. Paste your polarisation data, pick the range, and the calculator returns b, j₀ and R² with the plot.
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At a glance
| Model | η = a + b·log10|j|, least squares over the range you choose |
|---|---|
| Gives | Tafel slope (mV/dec), j₀ = 10^(−a/b), R², apparent α·n |
| Input | E vs RHE (OER, HER or your equilibrium) or η, with current density |
| Output | Tafel plot (PNG, SVG) and fit with all points (CSV) |
| Limits | Valid only on the linear part: away from η = 0 and from mass-transport limits |
| Runs in | Your web browser; nothing is uploaded |
| Price | Free, no account needed |
What it does
How to use the tafel slope calculator
- Paste the polarisation curveOne row per point: potential (or overpotential) and current density, from an iR-corrected, slow-scan LSV.
- Set the scaleChoose whether the first column is E vs RHE or η, the units, and the reaction (OER 1.23 V, HER 0 V, or your own equilibrium potential).
- Choose the linear regionEnter the |η| range of the straight part of the Tafel plot, away from η = 0 and below the mass-transport limit.
- Read the resultRead the Tafel slope, j₀ and R², and check the fitted line on the plot.
- ExportDownload the Tafel plot (PNG, SVG) and the fit (CSV), and report the range you used.
How it works
Classical Tafel analysis plots log|j| against the overpotential η, 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
η = a + b·log10|j|
by least squares over the |η| 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 η = 0 gives the exchange current density, log10 j₀ = −a/b, the current at which the forward and backward reactions are equal at equilibrium. j₀ comes out in the unit of your current column.
The slope relates to the transfer coefficient through b = ln10·RT/(α·n·F), 59.16 mV/dec for α·n = 1 at 298.16 K; the calculator reports the apparent α·n = ln10·RT/(F·|b|) at the temperature you enter (R = 8.314 J mol⁻¹ K⁻¹, F = 96 485 C 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 |η| 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 η → 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.
Worked example (illustrative data)
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 |η| = 260–320 mV (4 points) gives a Tafel slope of 79.4 mV/dec, R² = 0.998, intercept a = 236.9 mV, and an exchange current density of 1.04 × 10⁻³ mA cm⁻² (log10 j₀ = −2.98). The apparent α·n is 0.745 at 25 °C.
Frequently asked questions
How do you calculate a Tafel slope?
Plot the overpotential against log10 of the current density and fit a straight line to the linear part: η = a + b·log10|j|. The slope b, in mV per decade, is the Tafel slope.
How do I get the exchange current density from a Tafel plot?
Extrapolate the fitted Tafel line to η = 0: log10 j₀ = −a/b, where a is the intercept and b the slope. j₀ has the unit of your current density.
Which part of the curve should I fit?
Only the straight part of the Tafel plot: far enough from equilibrium that the reverse reaction no longer contributes, and below the currents where mass transport limits the rate. Different valid ranges can give different slopes, so report the range you used.
Should I use iR-corrected data?
Yes. Tafel analysis assumes the measured current reflects only the interfacial reaction; the voltage lost across the uncompensated solution resistance adds to the apparent overpotential and inflates the slope at high current.
What does a Tafel slope of 59 or 120 mV/dec mean?
At 25 °C, b = 59.16/(α·n) mV/dec, so 59 mV/dec corresponds to α·n = 1 and 120 mV/dec to α·n ≈ 0.5. What that implies about the mechanism depends on the reaction and needs more than the slope alone.
Can I use potential vs RHE instead of overpotential?
Yes. Choose “Potential vs RHE” and the reaction: the calculator subtracts 1.23 V for the OER, 0 V for the HER, or the equilibrium potential you type.
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