Overpotential & Tafel Calculator

Calculate current density from overpotential using the Butler-Volmer and Tafel equations.

Typically 0.3-0.7
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What Overpotential Buys You

At equilibrium an electrode still exchanges current in both directions — the exchange current density j0 — with no net flow. Applying overpotential tips that balance, and the Butler–Volmer equation describes by how much.

j = j0eαnFη/RT   (high overpotential limit)

Because the relationship is exponential, small changes in overpotential produce large changes in current. The Tafel slope quantifies this: at 25°C with α = 0.5 and n = 1, it is about 118 mV per decade — meaning 118 mV of extra overpotential multiplies current tenfold.

Electrode / reactionj0 (A/m²)Overpotential needed for 1 A/m²
H2 on platinum~10−3Very low — excellent catalyst
H2 on iron~10−6Moderate
H2 on mercury~10−12Very high — poor catalyst
O2 evolution~10−9High — four-electron process

That nine-order span between platinum and mercury is why catalyst choice dominates electrolyser efficiency. Oxygen evolution is intrinsically sluggish because it requires four electrons and O–O bond formation, which is why it contributes most of the overpotential in water splitting.

A lower Tafel slope is better: it means less extra voltage is needed for each tenfold current increase. Slope also reveals mechanism, since different rate-determining steps give characteristic values of 30, 40 or 120 mV per decade.

Worked Examples

Example 1: HER on Pt: j0=1e-3, η=100mV, α=0.5
j=j0×exp(0.5×38.9×0.1)
Result: j~0.192 A/m² — significant current
High j0 makes Pt good catalyst
Example 2: HER on iron: j0=1e-6, η=100mV
j=1e-6×exp(1.946)
Result: j~7e-6 A/m² — poor catalyst
1000× lower than Pt at same overpotential
Example 3: Reading mechanism from slope
Measured Tafel slope of 30 mV/decade
Result: Indicates a specific rate-determining step
Slopes near 120, 40 and 30 mV/decade correspond to different limiting steps in multi-electron mechanisms, making Tafel analysis a mechanistic tool.
Example 4: Why oxygen evolution is costly
j0 around 10−9 A/m² on most oxides
Result: Several hundred mV of overpotential needed
The four-electron process with O–O bond formation is intrinsically slow. This single reaction accounts for most inefficiency in water electrolysis.

Common Mistakes

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Assuming a large j0 means high current

Exchange current density is the equilibrium exchange rate with zero net current. It measures kinetic facility, not delivered current.

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Using the Tafel approximation at low overpotential

The simplified exponential form applies only above about 50–100 mV. Near equilibrium the full Butler–Volmer equation with both terms is required.

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Ignoring mass transport limits

At high current density, reactant supply rather than kinetics becomes limiting. Tafel behaviour flattens into a limiting current plateau.

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Confusing overpotential with cell voltage

Overpotential is the excess beyond equilibrium potential for one electrode. Cell voltage includes both electrodes plus ohmic losses.

Frequently Asked Questions

Tafel slope significance?
b=2.303RT/αF≈120mV/decade (α=0.5 at 25°C). Each 120mV overpotential: 10× current increase. Lower Tafel slope = more efficient electrocatalyst. Pt HER: b≈30mV/decade (different mechanism). Used to identify rate-determining step.
Exchange current density j₀ meaning?
j₀ is the intrinsic rate of forward and reverse reactions at equilibrium (no net current). High j₀ = good electrocatalyst. Pt for HER: j₀~1-10 mA/cm². Fe for HER: j₀~0.001 mA/cm². 3-4 orders of magnitude difference.
What is exchange current density?
The equal forward and reverse current at equilibrium, where net current is zero. It measures how kinetically facile a reaction is on a given electrode.
What does the Tafel slope tell you?
How much extra overpotential is needed for each tenfold increase in current. Lower is better, and the specific value reveals the rate-determining step.
Why is platinum such a good hydrogen catalyst?
Its exchange current density for hydrogen evolution is around 10−3 A/m² — roughly nine orders of magnitude above mercury — so very little overpotential is needed.
When does Tafel behaviour break down?
At low overpotential, where the full Butler–Volmer equation is needed, and at high current density where mass transport rather than kinetics limits the rate.

Formula Explorer connections

Interpretation: This formula links electron transfer, charge, potential, current or ionic transport in an electrochemical system. Assumption: Balance electron count and half-reactions, preserve sign conventions, and use consistent concentration, temperature and electrical units. Real cells include losses and overpotential.

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