Nernst Equation Calculator – Free Calculator

Understanding the Nernst equation calculator — concept and principle

The Nernst equation gives the actual voltage of an electrochemical cell or electrode when concentrations are not at standard values. It is used to predict battery and galvanic cell voltages, to understand pH and ion-selective electrodes, to work out membrane potentials in physiology, and to link cell voltage with the Gibbs energy of a reaction.

With little Zn²⁺ and plenty of Cu²⁺ (Q = 0.01), the cell gives 1.159 V, about 59 mV above E°.

How it is calculated

E = E° − (RT / nF) × ln Q

ΔG = −nFE

E° is the standard cell potential in volts, n the number of electrons transferred per reaction as written, Q the reaction quotient (products over reactants, each raised to its coefficient, using activities or, approximately, concentrations), and T the temperature, entered in °C and converted to kelvin. R = 8.314462618 J/(mol·K) and F = 96485.33212 C/mol. ΔG is shown in kJ/mol. At 25 °C the equation is often written E = E° − (0.05916/n) log₁₀ Q.

The principle

Gibbs energy of a reaction depends on composition: ΔG = ΔG° + RT ln Q. Electrical work and Gibbs energy are linked by ΔG = −nFE, because moving n moles of electrons through a potential E does nFE of work. Dividing the first equation by −nF gives the Nernst equation. When Q is below 1 (more reactants than at standard state) the reaction is more favourable and E rises; when Q exceeds 1, E falls. At equilibrium E = 0 and Q equals the equilibrium constant K.

Worked example

Default: a Daniell cell (Zn | Zn²⁺ || Cu²⁺ | Cu) with Q = [Zn²⁺]/[Cu²⁺] = 0.01.

Inputs: E° = 1.10 V, n = 2, Q = 0.01, T = 25 °C = 298.15 K.
RT/(nF) = 8.314462618 × 298.15 ÷ (2 × 96485.33212) = 0.012846 V.
ln 0.01 = −4.60517, so the correction is −0.012846 × (−4.60517) = +0.05916 V.
E = 1.10 + 0.05916 = 1.1592 V.
ΔG = −2 × 96485.33212 × 1.15916 ÷ 1000 = −223.68 kJ/mol.

Each point is the calculator re-run with only “Standard potential E° (V)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Standard potential E° (V)	Cell potential E (V)
0.275	0.3341593497
0.55	0.6091593497
0.825	0.8841593497
1.1	1.15915935
1.38	1.43415935
1.65	1.70915935
2.2	2.25915935

How to read the result

A positive E (negative ΔG) means the cell reaction is spontaneous as written. Each tenfold change in Q shifts E by 59.16/n mV at 25 °C. A negative E means the reverse reaction is spontaneous.

Common mistakes

Inverting Q (reactants over products).
Using the wrong n; it is the electrons in the balanced overall reaction.
Using log₁₀ with the RT/nF coefficient, or ln with 0.05916.
Including pure solids and the solvent in Q; their activity is 1.

Keep in mind: Concentrations stand in for activities, which is only accurate for dilute solutions. Real cells also lose voltage to internal resistance and overpotential when current flows.

Frequently asked questions

How do I get the equilibrium constant from E°?

Set E = 0: ln K = nFE°/(RT). For the Daniell cell this gives K of about 10³⁷.

Why does a pH electrode give about 59 mV per pH unit?

pH is a log₁₀ of H⁺ activity and n = 1, so the Nernst slope at 25 °C is 59.16 mV per decade.

Does temperature matter much?

The slope RT/nF grows by about 0.34% per kelvin near room temperature, and E° itself can also change.

Sources: IUPAC Green Book, Quantities, Units and Symbols in Physical Chemistry (electrochemistry) · A. J. Bard and L. R. Faulkner, Electrochemical Methods, Wiley

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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