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Nernst Equation Calculator

Calculate cell potential with the Nernst equation from the standard potential E°, electrons transferred, temperature, and the reaction quotient Q (or product and reactant concentrations) — or solve backward for Q from a measured potential. Also returns ΔG, ΔG°, the equilibrium constant K, and the voltage change per tenfold change in Q (59.16/n mV at 25°C).

Input

Standard cell potential, E°cathode − E°anode. Zinc–copper (Daniell) cell: 1.10 V.

Scientific notation (e.g. 1e-3) is accepted.

Output

Result
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curl -X POST https://api.iotools.cloud/v1/tool/nernst-equation-calculator \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "solveFor": "e",
    "standardPotential": "1.10",
    "electrons": "2",
    "temperature": "25",
    "temperatureUnit": "c",
    "quotientInput": "q",
    "qValue": "1000",
    "productTerm": "1",
    "reactantTerm": "0.001",
    "cellPotential": "1.0112"
  }'

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Guides

The Nernst Equation Calculator gives the actual potential of an electrochemical cell or half-cell under non-standard conditions. Enter the standard potential E°, the number of electrons transferred, the temperature, and the reaction quotient Q, and it returns the cell potential E. It also returns the Gibbs free energy, the equilibrium constant, and whether the reaction runs spontaneously. You can also run it in reverse: enter a measured potential and get Q back.

The equation

E = E° − (RT / nF) · ln Q
  = E° − (2.302585 · RT / nF) · log10 Q
  • E°: standard cell potential in volts (E°cathode − E°anode)
  • n: moles of electrons transferred in the balanced reaction
  • T: temperature in kelvin
  • R = 8.314462618 J/(mol·K), F = 96485.33212 C/mol
  • Q: reaction quotient, products over reactants, each raised to its coefficient

At 25°C the factor 2.302585·RT/F is 0.05916 V. That is the familiar "59 mV per decade" rule: each tenfold change in Q shifts E by 59.16/n mV.

How to use it

  1. Solve for the cell potential E (the usual direction) or the reaction quotient Q.
  2. Enter E° in volts and the electrons transferred n.
  3. Enter the temperature in °C, K or °F. It is converted to kelvin for you.
  4. Give Q either as a single Q value or as a product term and reactant term. The calculator divides them for you. Pure solids and liquids have an activity of 1, so leave them out.
  5. When solving for Q instead, enter the measured cell potential.

Example: Daniell cell

Zn(s) + Cu²⁺ → Zn²⁺ + Cu(s), E° = 1.10 V, n = 2, with [Zn²⁺] = 1 M and [Cu²⁺] = 0.001 M, so Q = 1000:

slope = 0.05916 / 2 = 0.02958 V per decade
E = 1.10 − 0.02958 × log10(1000) = 1.10 − 0.0887 = 1.0113 V

The cell still runs spontaneously, but at about 89 mV less than standard.

What the results show

  • Cell potential E and its shift from E°
  • Q and log10 Q
  • RT/nF and the slope per decade of Q at your temperature
  • ΔG = −nFE and ΔG° = −nFE° in kJ/mol
  • Equilibrium constant K = 10^(nFE° / 2.302585·RT). Very large K values are shown in scientific notation without overflowing.
  • A verdict: spontaneous (E > 0), non-spontaneous (E < 0), or at equilibrium (E = 0)

The steps box shows each substitution, and the results table can be downloaded as CSV.

FAQ

Should I use concentrations or activities?

The Nernst equation strictly uses activities. For dilute solutions (below about 0.1 M), molar concentration is a good approximation. For gases, use partial pressure in bar.

Why does E shift the other way when I swap Q?

Q above 1 means the mixture is product-heavy, which pushes E below E°. Q below 1 raises E above E°. When E reaches 0, Q equals K and the cell is at equilibrium: a dead battery.

To find [H⁺] from a pH reading before working out a hydrogen-electrode Q, use the pH Calculator. To make up a solution at a target concentration, use the Molarity Calculator.

Privacy

The calculation runs entirely in your browser.

cell potentialelectrode potentialreduction potentialelectrochemistryreaction quotientgalvanic cellgibbs free energyequilibrium constantemfchemistry

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