Nernst Equation formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| E | Cell potential | V | Cell (or half-cell) potential under actual conditions |
| E° | Standard potential | V | Standard potential at 1 M, 1 bar |
| T | Temperature | K | Absolute temperature |
| n | Electrons transferred | — | Number of electrons transferred in the balanced reaction |
| Q | Reaction quotient | — | Reaction quotient (products over reactants, as activities) |
What is Nernst Equation?
Nernst Equation: The potential of an electrochemical cell depends on the standard potential, the temperature, and the ratio of product to reactant activities. — Walther Nernst, 1889
The Nernst equation corrects a standard electrode potential for real concentrations and temperature. F = 96 485 C/mol is the Faraday constant. At 25 °C the factor RT/F ≈ 25.69 mV, giving the common form E = E° − (0.05916 V / n) log₁₀ Q.
It underlies pH electrodes and ion-selective electrodes, battery voltage versus state of charge, and the membrane potentials of nerve cells. For a single ion across a membrane the Nernst potential is E = (RT/zF) ln(Cout/Cin).
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
A Daniell cell (Zn | Zn²⁺ ‖ Cu²⁺ | Cu, E° = 1.10 V, n = 2) has [Zn²⁺]/[Cu²⁺] = 0.01 at 25 °C.
- RT/nF = 8.314 × 298.15 / (2 × 96 485) = 0.01285 V.
- E = 1.10 − 0.01285 × ln(0.01) = 1.10 + 0.0592 = 1.159 V.
Frequently asked questions
What happens when E = 0?
The cell is at equilibrium and Q equals the equilibrium constant K, so E° = (RT/nF) ln K. A "dead" battery has reached this state.
Should I use concentrations or activities?
Strictly activities. In dilute solutions, molar concentrations (and partial pressures in bar for gases) are a good approximation.