Nernst Equation Calculator
By Santaji GadepatilinUpdated October 27, 2026
The Nernst equation gives the voltage of an electrode or cell when concentrations are not standard. It explains how a pH sensor works — and why its slope matters when troubleshooting pH sensors.
How to use the Nernst equation calculator
Enter the standard potential E°, the number of electrons transferred, the temperature and the reaction quotient Q (products over reactants, each raised to its coefficient). The calculator gives the cell potential.
The Nernst equation
E = E° − (RT ÷ nF) × ln Q
with R = 8.314 J/(mol·K) and F = 96,485 C/mol. At 25 °C this becomes E = E° − (0.05916 ÷ n) log₁₀ Q.
Example: Daniell cell (Zn/Cu, E° = 1.10 V)
Zn | Zn²⁺ (0.01 M) ∥ Cu²⁺ (1 M) | Cu, so Q = [Zn²⁺] ÷ [Cu²⁺] = 0.01:
E = 1.10 − (0.05916 ÷ 2) × log₁₀(0.01) = 1.159 V
How Q changes the potential (n = 2, 25 °C)
| Q | E − E° |
|---|---|
| 0.0001 | +118.3 mV |
| 0.01 | +59.2 mV |
| 0.1 | +29.6 mV |
| 1 | -0.0 mV |
| 10 | -29.6 mV |
| 100 | -59.2 mV |
| 10000 | -118.3 mV |
Each tenfold change in Q shifts E by 59.16 ÷ n mV at 25 °C.
pH electrodes
For the hydrogen electrode, n = 1 and the Nernst slope is 59.16 mV per pH unit at 25 °C, rising with temperature (about 61.5 mV at 37 °C). pH meters use temperature compensation for this reason.
Membrane potentials
In biology, the Nernst equation gives the equilibrium potential for an ion across a cell membrane. For potassium (about 140 mM inside, 5 mM outside) at 37 °C, it is about −89 mV.
Frequently asked questions
What is the Nernst equation?
E = E° − (RT ÷ nF) ln Q. It gives the electrode or cell potential when concentrations are not 1 M.
What is the simplified form at 25 °C?
E = E° − (0.05916 ÷ n) log₁₀ Q.
What happens at equilibrium?
The cell potential falls to zero and Q equals the equilibrium constant K. Then E° = (RT ÷ nF) ln K.
How is the Nernst equation used in pH meters?
A glass electrode’s potential changes by about 59 mV per pH unit at 25 °C, as the Nernst equation predicts for hydrogen ions.