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chemistry

Nernst Equation Calculator

Calculate the cell potential under non-standard conditions using the Nernst equation.

Reviewed by Christopher FloiedPublished Updated

This free online nernst equation calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Results

Cell Potential E (V)

1.1592 V

How to Use This Calculator

1

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Fill in all required input fields for the Nernst Equation Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

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Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

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4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Nernst Equation Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

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About Nernst Equation Calculator

The Nernst equation calculator determines the electrochemical cell potential under non-standard conditions by accounting for the concentrations (activities) of the reactants and products. While the standard cell potential E° applies only when all species are at unit activity (1 M, 1 atm), real electrochemical cells operate at varying concentrations. The Nernst equation modifies E° using the reaction quotient Q to give the actual cell potential E. This is essential for understanding batteries, corrosion, electroplating, sensors, and biological membrane potentials.

The Math Behind It

The Nernst equation is derived from the relationship between Gibbs free energy and cell potential: ΔG = −nFE. Under non-standard conditions, ΔG = ΔG° + RT ln(Q), so E = E° − (RT/nF) ln(Q). At 25 °C (298.15 K), RT/F = 0.02569 V, giving the simplified form E = E° − (0.02569/n) ln(Q). Using log base 10 instead of natural log: E = E° − (0.05916/n) log₁₀(Q). The reaction quotient Q has the same form as the equilibrium constant K but uses current (not equilibrium) concentrations. When Q < K, E > 0 and the cell produces electricity (galvanic cell). When Q > K, E < 0 and external power is needed (electrolytic cell). At equilibrium, Q = K and E = 0. The Nernst equation is also used in biology: the resting membrane potential of neurons is governed by the Nernst equation applied to individual ion channels, most notably K⁺ and Na⁺ across the cell membrane.

Formula Reference

Nernst Equation

E = E° − (RT/nF) × ln(Q)

Variables: E = cell potential (V); E° = standard potential; R = 8.314 J/(mol·K); T = temperature (K); n = electrons; F = 96485 C/mol; Q = reaction quotient. At 25 °C: E = E° − (0.02569/n) × ln(Q)

Worked Examples

Example 1: Daniell cell (Zn/Cu)

E° = 1.10 V, n = 2, Q = 0.01 (dilute Zn²⁺, concentrated Cu²⁺), T = 298 K.

Step 1:RT/nF = (8.314 × 298) / (2 × 96485) = 0.01285 V.
Step 2:ln(0.01) = −4.605.
Step 3:E = 1.10 − (0.01285)(−4.605) = 1.10 + 0.0592 = 1.159 V.

The cell potential is approximately 1.16 V under these conditions.

Common Mistakes & Tips

  • !Using log₁₀ with the natural-log version of the equation (or vice versa) — the numerical prefactor differs.
  • !Getting the sign of Q wrong — products go in the numerator, reactants in the denominator.
  • !Forgetting to use Kelvin for temperature.

Related Concepts

Gibbs Free Energy

ΔG = −nFE connects electrochemistry to thermodynamics.

Used in These Calculators

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Frequently Asked Questions

What happens when Q = 1?

When Q = 1, ln(Q) = 0, so E = E°. This is the standard-state condition where all reactants and products are at unit activity.

Can I use this for half-cells?

Yes. The Nernst equation applies to individual half-reactions as well as full cells. Use the half-reaction E° and the relevant ion concentrations.

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