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Nernst equation calculator

This Nernst equation calculator gives the cell potential for any concentrations. Example: the Daniell cell (E° = 1.10 V, n = 2) has E = 1.07042 V at 25 °C and Q = 10.

Example: Reaction quotient given as: Reaction quotient Q directly · Standard potential E° 1.1 V · Electrons transferred n 2 e⁻ · Temperature 25 °C · Reaction quotient Q 10 → Result: E = 1.07042 V (cell potential). Source: NIST CODATA 2022: molar gas constant R = 8.314462618 J/(mol K), Faraday constant F = 96 485.33212 C/mol. Updated: .

V
Standard cell potential (cathode minus anode) in volts, e.g. Daniell cell 1.10 V.
e⁻
Whole number from the reaction equation, e.g. 2 for Zn + Cu²⁺.
°C
Products over reactants, each raised to its coefficient; solids and water are omitted.
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Result

Result
E = 1.07042 V (cell potential)
All representations
QuantityValue
Cell potential E1.07042 V
Reaction quotient Q10
Gibbs energy of reaction ΔG-206.56 kJ/mol
Slope per decade of Q29.5797 mV
Temperature298.15 K
Calculation steps
  • E = E° − (R·T) / (n·F) · ln Q = 1.1 − (8.314462618 · 298.15) / (2 · 96,485.33212) · ln(10) = 1.07042 V.
  • ΔG = −n·F·E = −2 · 96,485.33212 C/mol · 1.07042 V = -206.56 kJ/mol.
Valid for ideally dilute solutions (activities ≈ concentrations). For E > 0 and ΔG < 0 the reaction is spontaneous. For several species enter Q directly (concentrations raised to their coefficients).

How it is calculated

The Nernst equation gives the voltage of a galvanic cell, or the potential of a half-cell, at any concentrations. It links the standard potential E° with the reaction quotient Q and the temperature.

Formula

E = E° − (R·T) / (n·F) · ln Q with the gas constant R = 8.314462618 J/(mol·K), the Faraday constant F = 96,485.33212 C/mol (CODATA 2022), the absolute temperature T in kelvin and the number n of electrons transferred. Q is the quotient of product and reactant concentrations. The Gibbs energy of reaction is ΔG = −n·F·E.

Worked example

Daniell cell: E° = 1.10 V, n = 2, T = 25 °C = 298.15 K, Q = 10. Then R·T/(n·F) = 0.0128463 V, and E = 1.10 − 0.0128463 · ln 10 = 1.07042 V. For every power of ten in Q, E changes by 29.5797 mV; for n = 1 it is 59.16 mV, the well-known 59 mV rule. The Gibbs energy is ΔG = −2 · 96,485.33212 · 1.07042 V = -206.56 kJ/mol. With Q = 0.1 the voltage rises to 1.12958 V; at Q = 1, E = E° = 1.1 V.

Frequently asked questions

What is the Nernst equation used for?

To calculate cell voltages and electrode potentials at concentrations that differ from the standard state of 1 mol/L, for example for pH, batteries or ion-selective electrodes.

What is the 59 mV rule?

At 25 °C and one electron transferred, the potential changes by 59.16 mV for every tenfold change in concentration; for n = 2 it is half of that.

Why must the temperature be in kelvin?

Because R·T contains the absolute temperature. The calculator adds 273.15 to the °C you enter (25 °C gives 298.15 K).

Sources and legal basis

As of: · Editorial policy

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