Nernst Equation Calculator

Calculate cell potential at non-standard conditions using the Nernst equation E=E°-(RT/nF)lnQ.

Standard cell potential E° (V) (V)

Number of electrons transferred n

Reaction quotient Q

Temperature T (K) (K)

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Why Concentration Changes Voltage

Standard cell potentials assume every species is at 1 M and 1 atm. Real cells almost never are, and the Nernst equation corrects for it. The physical reason is simply Le Chatelier: a cell further from equilibrium has more driving force, so it produces more voltage.

E = E° − (RT/nF) ln Q or at 298 K E = E° − (0.05916/n) log Q

Term	Meaning	Note
E°	Standard cell potential	At 1 M, 1 atm, 298 K
n	Electrons transferred	From the balanced redox equation
Q	Reaction quotient	Products over reactants, current values
0.05916	RT/F × ln(10) at 298 K	Only valid at 25°C

The direction of the effect follows from the sign. When Q is small — plenty of reactant, little product — log Q is negative, so E rises above E°. As the cell discharges, products build up, Q increases, and voltage falls. When Q reaches K, E becomes zero and the battery is flat. That is the precise electrochemical meaning of a dead battery: not empty, but at equilibrium.

Concentration Cells

A striking consequence is that a cell can generate voltage with identical electrodes in the same electrolyte, differing only in concentration. Here E° = 0, so the entire potential comes from the log term. Every tenfold concentration difference produces 59.16 mV per electron transferred.

Concentration ratio	n = 1	n = 2
10:1	59.2 mV	29.6 mV
100:1	118.3 mV	59.2 mV
1000:1	177.5 mV	88.7 mV

This is the operating principle of the pH electrode. A glass membrane separates the sample from an internal solution of fixed pH, and the resulting potential is proportional to the pH difference — about 59 mV per pH unit at 25°C. It is also why pH meters need temperature compensation: the 59.16 factor scales with absolute temperature, reaching about 61.5 mV per unit at 37°C.

Worked Examples

Example 1: Zn-Cu cell: E°=1.10V, n=2, Q=[Zn2+]/[Cu2+]=0.001

E=1.10-(0.05916/2)×log(0.001)

Result: E=1.10+0.0887=1.189V

Lower Q → higher cell potential

Example 2: Concentration cell: E°=0, n=1, Q=0.01

E=0-(0.05916/1)×log(0.01)

Result: E=0.1183V

Concentration difference drives cell even at E°=0

Example 3: Battery approaching flat

Cell with E° = 1.10 V, n = 2, discharged until Q = 10⁶

Result: E = 1.10 − 0.02958 × 6 = 0.92 V

Voltage sags as products accumulate. When Q eventually reaches K, E hits zero — the cell is at equilibrium and delivers no more work.

Example 4: pH electrode response

Concentration cell, n = 1, one pH unit difference

Result: 59.2 mV

Each pH unit is a tenfold difference in [H⁺], giving 59.16 mV at 25°C. This linear relationship is what makes potentiometric pH measurement possible.

Example 5: Temperature dependence

Same electrode at 37°C instead of 25°C

Result: 61.5 mV per pH unit

The slope scales with absolute temperature: 0.05916 × (310/298). Uncompensated, this introduces a systematic error in physiological measurements.

Common Mistakes

⚠️

Using 0.05916 at temperatures other than 25°C

That constant is RT/F multiplied by ln(10) evaluated at 298 K. At other temperatures recompute it, or use the RT/nF form directly with T in kelvin.

⚠️

Getting the sign of the log term wrong

The term is subtracted. A small Q gives a negative logarithm, so subtracting it increases E. Sign errors here flip the predicted direction of the concentration effect.

⚠️

Using the wrong n

n is the number of electrons in the balanced overall reaction, not per half-reaction as written in tables. Getting it wrong scales the entire correction incorrectly.

⚠️

Including solids and pure liquids in Q

As with any equilibrium expression, pure solids and liquids are omitted. Electrode metals themselves never appear in Q.

Frequently Asked Questions

Nernst at equilibrium?

At equilibrium Q=K and E=0. Therefore 0=E°-(RT/nF)lnK → lnK=nFE°/RT. This connects electrochemistry to thermodynamics: E°>0 means K>1 (products favored).

Biological Nernst equation?

Membrane potential: E=(RT/zF)ln([ion]outside/[ion]inside). For K+ at 37°C with [K+]out=5mM, [K+]in=140mM: E=(0.02585/1)×ln(5/140)=-87mV. Close to resting membrane potential.

What does the Nernst equation calculate?

The actual cell potential under non-standard concentrations, correcting the standard potential for the reaction quotient and temperature.

Why does battery voltage drop as it discharges?

Products accumulate and reactants deplete, raising Q. Since the log term is subtracted, rising Q lowers E. At Q = K the potential reaches zero.

How can a cell with E° = 0 produce voltage?

In a concentration cell, both electrodes are identical so E° is zero, but a concentration difference makes Q differ from 1. The entire potential comes from the log term.

Where does 59.16 mV come from?

It is 2.303RT/F at 298 K, converting the natural log form to base 10. It gives the potential change per tenfold concentration ratio for a one-electron process.

Why do pH meters need temperature compensation?

The Nernst slope is proportional to absolute temperature — 59.16 mV per pH unit at 25°C but 61.5 at 37°C. Without correction, readings drift systematically.

Formula Explorer connections

Interpretation: This formula links electron transfer, charge, potential, current or ionic transport in an electrochemical system. Assumption: Balance electron count and half-reactions, preserve sign conventions, and use consistent concentration, temperature and electrical units. Real cells include losses and overpotential.

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