Last updated: 2026-06-16

The Gibbs free energy change $\Delta G$ tells you whether a reaction is spontaneous and how much useful work it can do. For a redox reaction running in an electrochemical cell, that free energy is carried by electrons moving through a potential difference, so it can be read directly from the cell's voltage. This calculator turns a measured or standard cell potential into $\Delta G$, the bridge between electrochemistry and thermodynamics that students meet when they connect cell voltages to spontaneity.

Energy carried by the electrons

When $n$ moles of electrons move through a potential $E$, the electrical work done is the charge times the voltage. One mole of electrons carries the Faraday constant $F = 96{,}485\ \mathrm{C/mol}$, so the free energy change is:

$\Delta G = -nFE$

The minus sign encodes the convention that a spontaneous reaction releases free energy. Because this product comes out in joules per mole, dividing by 1000 expresses the free energy in kilojoules per mole. Using the standard potential $E^\circ$ yields the standard free energy $\Delta G^\circ$.

Worked example

A Daniell cell transfers two electrons and has a standard potential of $1.10\ \mathrm{V}$:

The large negative value shows the reaction is strongly spontaneous and can release a substantial amount of energy as electrical work.

Why this formula works

Free energy is the maximum non-expansion work available from a process. In a cell, that work is electrical: charge $nF$ pushed through a voltage $E$. Equating the two gives $\Delta G = -nFE$ exactly. The same relationship runs in reverse — a known $\Delta G$ implies a cell voltage — which is how thermodynamic data and electrochemical measurements are cross-checked.

To find the cell potential itself from electrode tables, start with the Standard Cell Potential Calculator. Because $\Delta G^\circ$ also equals $-RT\ln K$, the free energy ties directly to the equilibrium position computed by the Equilibrium Constant from Cell Potential Calculator. For a non-electrochemical route to the same quantity, the Gibbs Free Energy Calculator uses enthalpy and entropy instead.