Nernst Equation Calculator

Calculate the cell potential of an electrochemical cell under non-standard conditions using the Nernst equation. Solve for E, E°, Q, n, or temperature.

⚡ Nernst Equation Calculator

Solve for:

Cell Potential (E) Standard Potential (E°) Reaction Quotient (Q) Electrons Transferred (n)

Standard Cell Potential (E°)

Standard reduction potential of the cell reaction

Temperature (T)

Number of Electrons Transferred (n)

From the balanced half-reaction

Reaction Quotient (Q)

Q = [products] / [reactants]; enter value or use scientific notation (e.g. 1e-4)

Cell Potential (E)

Common Half-Cell Presets

✅ Result

What Is the Nernst Equation?

The Nernst equation is one of the most fundamental equations in electrochemistry. Named after the German chemist Walther Nernst (1864–1941), it relates the reduction potential of an electrochemical cell to the standard electrode potential, temperature, and the activities (concentrations) of the chemical species involved in the reaction.

Under standard conditions (all concentrations at 1 M, all gases at 1 atm, temperature at 25°C), the cell potential equals the standard cell potential E°. The Nernst equation tells us how E changes when conditions deviate from standard.

The Nernst Equation Formula

E = E° − (RT / nF) × ln(Q)

Or equivalently, using base-10 logarithm at 25°C (298.15 K):

E = E° − (0.05916 / n) × log₁₀(Q)

Where:

E — Cell potential under non-standard conditions (V)
E° — Standard cell potential (V)
R — Universal gas constant = 8.314 J/(mol·K)
T — Absolute temperature (K)
n — Number of moles of electrons transferred in the balanced reaction
F — Faraday constant = 96,485 C/mol
Q — Reaction quotient = [products]/[reactants]

The 0.05916 Factor

At exactly 25°C (298.15 K), the factor RT/F × ln(10) evaluates to:

(8.314 × 298.15) / 96485 × 2.3026 = 0.05916 V

This simplification makes calculations much easier when working at room temperature, allowing you to use log₁₀ instead of the natural logarithm.

Standard Electrode Potentials

The standard cell potential E° is calculated from the standard reduction potentials of the two half-cells:

E°_cell = E°_cathode − E°_anode

Half-Reaction	E° (V)
Li⁺ + e⁻ → Li	−3.04
Na⁺ + e⁻ → Na	−2.71
Al³⁺ + 3e⁻ → Al	−1.66
Zn²⁺ + 2e⁻ → Zn	−0.76
Fe²⁺ + 2e⁻ → Fe	−0.44
Ni²⁺ + 2e⁻ → Ni	−0.26
2H⁺ + 2e⁻ → H₂	0.00 (reference)
Cu²⁺ + 2e⁻ → Cu	+0.34
Ag⁺ + e⁻ → Ag	+0.80
Au³⁺ + 3e⁻ → Au	+1.50
F₂ + 2e⁻ → 2F⁻	+2.87

How to Use the Nernst Equation

Write the balanced redox reaction and identify the half-reactions.
Determine E° from the table of standard reduction potentials: E°_cell = E°_cathode − E°_anode.
Count n — the number of electrons transferred in the balanced equation.
Calculate Q — the reaction quotient using actual concentrations.
Plug into the Nernst equation and solve for E.

Example: Daniell Cell

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

Given: E° = 1.10 V, n = 2, [Zn²⁺] = 0.01 M, [Cu²⁺] = 1.0 M, T = 25°C

Step 1: Q = [Zn²⁺]/[Cu²⁺] = 0.01/1.0 = 0.01
Step 2: E = 1.10 − (0.05916/2) × log(0.01)
= 1.10 − 0.02958 × (−2) = 1.10 + 0.0592 = 1.159 V

The cell potential is higher than standard because Q < 1 (Le Chatelier: reaction favors products).

Reaction Quotient (Q)

The reaction quotient Q has the same form as the equilibrium constant K, but uses the current concentrations rather than equilibrium concentrations:

Q = [C]^c[D]^d / [A]^a[B]^b

Pure solids and liquids have an activity of 1 and are omitted from Q.
Aqueous species use molar concentrations.
Gases use partial pressures (in atm).
When Q = K (equilibrium), the Nernst equation gives E = 0, meaning the cell is “dead” (no driving force).

Nernst Equation at Equilibrium

At equilibrium, E = 0 and Q = K. Substituting into the Nernst equation:

0 = E° − (RT/nF) × ln(K)

Rearranging gives the important relationship between E° and K:

E° = (RT/nF) × ln(K) = (0.05916/n) × log(K) at 25°C

This connects thermodynamics (ΔG° = −nFE°) to the equilibrium constant and cell potential.

Applications of the Nernst Equation

Batteries: Predict voltage changes as a battery discharges (Q increases toward K).
Corrosion: Determine whether a metal will corrode under given environmental conditions.
pH electrodes: The glass electrode in a pH meter follows the Nernst equation, producing ~59.16 mV per pH unit at 25°C.
Concentration cells: Calculate the potential generated by a concentration difference alone (E° = 0).
Biological systems: The membrane potential of neurons follows the Nernst equation for ion gradients (Na⁺, K⁺, Cl⁻).
Electroplating: Determine required potentials for metal deposition.

Gibbs Free Energy and Cell Potential

The Nernst equation is directly linked to thermodynamics through:

ΔG = −nFE and ΔG° = −nFE°

If E > 0: ΔG < 0 → reaction is spontaneous (galvanic cell)
If E < 0: ΔG > 0 → reaction is non-spontaneous (electrolytic cell)
If E = 0: ΔG = 0 → system is at equilibrium

Frequently Asked Questions

What is the difference between E and E°?

E° is the standard cell potential measured under standard conditions (1 M concentrations, 1 atm, 25°C). E is the actual cell potential under the real conditions of the experiment. The Nernst equation connects the two.

Why does cell voltage decrease as a battery discharges?

As the reaction proceeds, products accumulate and reactants are consumed, increasing Q. Since the Nernst equation subtracts (RT/nF)ln(Q), a larger Q reduces E. When Q reaches K, E = 0 and the battery is dead.

Can the Nernst equation give negative potentials?

Yes. A negative E means the reaction as written is non-spontaneous. The reverse reaction would be spontaneous. In practice, you would need to supply external energy (electrolysis) to drive the reaction forward.

How does temperature affect cell potential?

Temperature appears directly in the Nernst equation as T. Higher temperature increases the (RT/nF)ln(Q) term, making the correction to E° larger. For reactions with Q > 1, higher temperature decreases E; for Q < 1, higher temperature increases E.