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Nernst Equation Calculator

Calculate electrode potential at non-standard concentrations

Oxidized Form (Ox)

Reduced Form (Red)

About the Nernst Equation

The Nernst equation relates electrode potential to the standard potential and the concentrations of chemical species involved. It shows how potential changes from standard conditions.

At 25°C: E = E° - (0.0592/n)log₁₀(Q)

A 10-fold change in concentration ratio changes the potential by ~59.2/n mV.

What Is the Nernst Equation?

The Nernst equation calculates the electrode potential of an electrochemical cell under non-standard conditions. It relates the actual cell potential to the standard electrode potential, temperature, number of electrons transferred, and the concentrations of reactants and products. Named after Walther Nernst (Nobel Prize in Chemistry, 1920), this equation is fundamental to electrochemistry and explains how concentration changes affect cell voltage.

Under standard conditions (1 M concentrations, 1 atm pressure, 25°C), every electrochemical half-reaction has a characteristic standard electrode potential (E°). The Nernst equation adjusts this standard potential for the actual concentrations present in the cell. When the reaction quotient Q equals 1 (all concentrations at standard values), the correction term vanishes and E equals E°. As concentrations deviate from standard, the cell potential shifts accordingly.

This calculator allows you to enter the standard electrode potential, temperature, number of electrons transferred, and the concentrations and stoichiometric coefficients of both the oxidized and reduced forms. It computes the electrode potential, the potential shift from standard conditions, and whether the cell is more oxidizing or reducing than at standard conditions.

The Nernst Equation

The Nernst equation relates electrode potential to the standard potential and the reaction quotient, accounting for the non-standard concentrations of all species involved.

Nernst Equation

E = E° − (RT/nF) × ln(Q)

Where:

  • E= Electrode potential at non-standard conditions (V)
  • E°= Standard electrode potential (V)
  • R= Universal gas constant (8.314 J/(mol·K))
  • T= Absolute temperature (K)
  • n= Number of electrons transferred in the half-reaction
  • F= Faraday constant (96,485 C/mol)
  • Q= Reaction quotient = [Red]^aRed / [Ox]^aOx

How to Use This Calculator

This calculator supports detailed Nernst equation calculations with stoichiometric coefficients:

  1. Enter Standard Electrode Potential (E°): Input the standard potential in volts for the half-reaction.
  2. Enter Temperature: Default is 298.15 K (25°C). Adjust for non-standard temperatures.
  3. Enter Electrons Transferred (n): The number of electrons in the balanced half-reaction.
  4. Enter Oxidized Form Details: Concentration in molarity and stoichiometric coefficient.
  5. Enter Reduced Form Details: Concentration in molarity and stoichiometric coefficient.
  6. View Results: The electrode potential, potential shift, reaction quotient, and condition (more oxidizing/reducing) are displayed.

Interpreting the Results

The electrode potential (E) is the actual voltage of the half-reaction at the given concentrations. A positive shift from E° means the cell is more oxidizing than at standard conditions; a negative shift means it is more reducing.

The reaction quotient Q quantifies how far the system is from equilibrium. When Q < 1 (more products relative to reactants at equilibrium), the ln(Q) term is negative, making E more positive than E°. When Q > 1, the correction is positive, making E less positive (or more negative) than E°.

The Nernst coefficient (RT/nF) determines the sensitivity of the potential to concentration changes. At 25°C with n = 1, this coefficient is 25.69 mV. A tenfold change in Q shifts the potential by 59.2/n mV at 25°C, which is a useful rule of thumb for quick estimates.

The condition indicator tells you whether the half-cell is more oxidizing (higher tendency to accept electrons) or more reducing (higher tendency to donate electrons) compared to standard conditions.

Real-World Applications

The Nernst equation is essential in battery design and analysis. The voltage of a battery changes as it discharges because reactant concentrations decrease and product concentrations increase. The Nernst equation predicts this voltage decline and helps engineers design batteries that maintain stable output over their useful life.

In biological systems, the Nernst equation calculates equilibrium potentials for ion channels across cell membranes. The resting membrane potential of neurons is determined by the Nernst potentials for K⁺, Na⁺, and Cl⁻ weighted by their membrane permeabilities.

In analytical chemistry, ion-selective electrodes use the Nernst equation to convert measured voltages into ion concentrations. pH meters, fluoride electrodes, and calcium sensors all rely on this relationship for quantitative measurements.

In corrosion science, the Nernst equation predicts which metals will corrode under specific environmental conditions and guides the design of cathodic protection systems for pipelines, ships, and bridges.

Worked Examples

Copper Half-Cell

Problem:

Calculate the electrode potential for Cu²⁺/Cu (E° = 0.34 V) with [Cu²⁺] = 0.01 M at 25°C and n = 2.

Solution Steps:

  1. 1Q = [Cu²⁺] = 0.01 (reduced form is solid Cu, activity = 1)
  2. 2E = E° − (RT/nF) × ln(Q) = 0.34 − (0.02569/2) × ln(0.01)
  3. 3E = 0.34 − 0.01285 × (−4.605) = 0.34 + 0.0592 = 0.399 V
  4. 4The potential shift is +59.2 mV, more oxidizing than standard

Result:

E = 0.399 V (+59.2 mV shift from standard, more oxidizing)

Concentration Cell

Problem:

A concentration cell has [Zn²⁺]₁ = 1.0 M and [Zn²⁺]₂ = 0.001 M. E° = 0 V for a concentration cell. Calculate the cell potential at 25°C.

Solution Steps:

  1. 1Q = [Zn²⁺]₂ / [Zn²⁺]₁ = 0.001 / 1.0 = 0.001
  2. 2n = 2 for Zn²⁺/Zn
  3. 3E = 0 − (0.02569/2) × ln(0.001) = −0.01285 × (−6.908)
  4. 4E = 0.0888 V

Result:

E = 0.0888 V (concentration difference drives the cell voltage)

Temperature Effect

Problem:

For a half-reaction with E° = 0.77 V and n = 1, what is E at 50°C (323.15 K) when Q = 10?

Solution Steps:

  1. 1RT/nF at 323.15 K = (8.314 × 323.15) / (1 × 96485) = 0.02786 V
  2. 2E = 0.77 − 0.02786 × ln(10) = 0.77 − 0.02786 × 2.303
  3. 3E = 0.77 − 0.0641 = 0.706 V

Result:

E = 0.706 V (higher temperature increases sensitivity to concentration)

Tips & Best Practices

  • ✓At 25°C, use the simplified form: E = E° − (0.0592/n) × log₁₀(Q) for quick calculations.
  • ✓A tenfold change in concentration ratio shifts potential by 59.2/n mV at 25°C.
  • ✓Remember: Q = [products] / [reactants], each raised to stoichiometric coefficients.
  • ✓For solid and pure liquid species, the activity is 1 — they don't appear in Q.
  • ✓Higher temperatures increase the sensitivity of potential to concentration changes.
  • ✓The potential shift indicates whether the cell is more oxidizing (positive shift) or reducing (negative shift) than standard.

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Frequently Asked Questions

The reaction quotient Q is the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients. For a half-reaction Ox + ne⁻ → Red, Q = [Red]^aRed / [Ox]^aOx. When Q = 1, the system is at standard conditions and E = E°. Q > 1 means excess products (lower driving force), while Q < 1 means excess reactants (higher driving force).
Temperature enters the equation through the RT/F factor. Higher temperatures increase the magnitude of the correction term, making the potential more sensitive to concentration changes. At 25°C, the factor RT/F ≈ 25.69 mV. At 37°C (body temperature), it increases to about 26.73 mV. The simplified form at 25°C is E = E° − (0.0592/n) × log₁₀(Q).
At 25°C, a tenfold change in the concentration ratio (Q changes by a factor of 10) shifts the potential by 59.2/n mV. For n = 1, this is 59.2 mV per decade. This rule is useful for quick estimates: if you halve the concentration of the oxidized form, the potential shifts by about +18 mV (for n = 1).
The Nernst equation assumes ideal solution behavior. At high ionic strengths (> 0.1 M), activity coefficients deviate significantly from 1, and the equation must be modified to use activities instead of concentrations. The Debye-Hückel equation or Pitzer equations can provide activity coefficient corrections for non-ideal solutions.
pH electrodes are based on the Nernst equation. The glass electrode responds to H⁺ activity, producing a voltage proportional to pH. At 25°C, each pH unit corresponds to a 59.16 mV change in potential. The relationship E = E° − (RT/F) × ln[H⁺] becomes E = constant + 59.16 × pH, allowing direct conversion of voltage to pH.

Sources & References

Last updated: 2026-06-06

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Editorial Note

MyCalcBuddy Editorial Team

This page is maintained as an educational calculator reference.

Source

Formula Source: Chemistry: The Central Science

by Brown, LeMay, Bursten

UpdatedLast reviewed: May 2026
CheckedFormula checks are based on standard references and internal QA review.