Equilibrium first, overpotential second
All equilibrium equations are written as reductions, even when evaluating oxygen evolution. A measured single-electrode potential is converted to the same reference as Eeq. Residual ohmic drop is then distinguished from the thermodynamic reference.
η = Einterface − Eeq
Eeq = E° − (RT/nF) ln Q
Current is positive for oxidation and negative for reduction. Thus negative cathodic current makes the corrected potential less negative. Enter the remaining uncompensated resistance only: applying the full resistance to data already corrected by the instrument double-counts that correction.
Water-reaction presets
For HER, the reduction is 2H⁺ + 2e⁻ ⇌ H₂ and log₁₀Q = log₁₀(fH₂/1 bar) + 2pH. For oxygen/water, O₂ + 4H⁺ + 4e⁻ ⇌ 2H₂O and log₁₀Q = 2log₁₀aH₂O − log₁₀(fO₂/1 bar) + 4pH. The oxygen/water preset uses E° = 1.229 V at 25 °C only.
Gas activities are expressed as fugacity divided by 1 bar. For an ideal-gas approximation, enter partial pressure in bar. The RHE scale remains referenced to unit H₂ fugacity; changing a reaction-gas input is not changing that reference electrode.
Worked example
OER, 1.550 V vs RHE, 25 °C, unit gas and water activities:
η = 1.550 − 1.229 = +0.321 V.
With I = +10 mA and remaining Ru = 5 Ω: η = +0.271 V.
Custom reactions, including CO₂ reduction
The general aqueous Nernst mode uses a reduction-form equation with n electrons and a net m protons consumed. Enter log₁₀Q excluding H⁺; the calculator adds m × pH. Supply E° at the actual temperature. Do not add this pH term again to a conditional potential that already includes pH.
For solvent-specific equilibria or complex CO₂ speciation, use Supplied Eeq in exactly the same reference and conditions as the measurement. There is no universal “CO₂-reduction overpotential” independent of product, activities, proton donor and solvent. This tool does not infer a thermodynamic equilibrium from an irreversible peak or onset.
Common questions
Why show both signed η and |η|?
The signed value identifies the direction. The magnitude alone can hide that a potential is on the wrong side of equilibrium for the intended reaction. A separate driving-potential check warns when the selected direction is not thermodynamically driven by the entered potential.
Can I enter a two-electrode cell voltage?
No. This calculator evaluates a single-electrode overpotential. A full cell includes both electrode contributions and ohmic losses. Nor does the result automatically separate kinetic from concentration overpotential: that depends on whether local or bulk activities define Eeq.
Sources and conventions
- IUPAC Gold Book · Overpotential
- IUPAC Gold Book · Nernst equation
- IUPAC Gold Book · Equilibrium electrode potential
- Tian & Anderson, J. Phys. Chem. C (2011) · O₂/H₂O standard potential
- Gamry Instruments · Understanding iR compensation
- ACS Omega (2021) · Reference-potential conventions, Table 2
Method version 1.0.0 · 19 September 2026. Display precision is not measurement accuracy. Read the full scope and validation limits.