Last updated: 2026-06-16

The equilibrium constant $K$ describes how far a reaction proceeds before the forward and reverse rates balance. For a redox reaction, that endpoint is fixed by the cell's standard potential: a larger driving voltage pushes the equilibrium further toward products. This calculator converts a standard cell potential into $K$, a step that appears whenever an electrochemistry course connects cell voltages to the equilibrium chapter.

From potential to equilibrium constant

Two expressions for the standard free energy can be set equal. Electrochemistry gives $\Delta G^\circ = -nFE^\circ$, and thermodynamics gives $\Delta G^\circ = -RT\ln K$. Equating them and solving for the constant:

$\ln K = \frac{nFE^\circ}{RT}, \qquad K = e^{nFE^\circ/RT}$

Here $n$ is the electrons transferred, $F = 96{,}485\ \mathrm{C/mol}$ is the Faraday constant, $R = 8.314\ \mathrm{J/(mol\cdot K)}$ is the gas constant, and $T$ is the absolute temperature.

Worked example

For a cell that transfers two electrons with $E^\circ = 1.10\ \mathrm{V}$ at 298.15 K:

A potential of only about 1 V produces an astronomically large $K$, meaning the reaction runs essentially to completion.

Why a small voltage gives an enormous K

The equilibrium constant sits inside an exponential, so it is exquisitely sensitive to the potential. At 25 °C the relation simplifies to $\ln K = nE^\circ/0.0257$, and every $0.0257/n\ \mathrm{V}$ multiplies $K$ by a factor of $e$. This is why electrochemical reactions with modest voltages can drive transformations far past what intuition suggests.

Temperature enters through the $RT$ term, so the same potential implies a different $K$ at a different temperature. To obtain the potential from electrode data first, use the Standard Cell Potential Calculator; for the free energy that links the two, see the Gibbs Free Energy from Cell Potential Calculator. When concentrations are not standard, the cell voltage itself shifts according to the Nernst Equation Calculator.