Nernst Equation Calculator
Calculate an electrode or cell reduction potential under non-standard conditions from temperature, electron transfer, and chemical activities.
Reaction conditions
Signed finite voltage. Example: 2.25.
Must correspond to a temperature above absolute zero.
A positive whole number from the balanced reaction.
Positive, dimensionless activity; concentration may be used as an approximation.
Positive, dimensionless activity in the denominator of the activity ratio.
Live result
Calculation breakdown
| Step | Expression | Value |
|---|---|---|
| Temperature conversion | T = °C + 273.15 | 298.15 K |
| Activity ratio | ared / aox | 0.100000 |
| Logarithmic term | ln(ared / aox) | – 2.302585 |
| Thermal factor | RT / zF | 0.012846 V |
| Reduction potential | E° – correction | 2.279579 V |
How to use this Nernst equation calculator
What this calculator does
This calculator estimates the equilibrium reduction potential of a half-cell or complete electrochemical reaction under specified non-standard conditions. It applies the Nernst equation to a standard reduction potential, absolute temperature, transferred-electron count, and the activities of the reduced and oxidized forms. The result is an equilibrium thermodynamic potential in volts. It does not predict reaction rate, electrode overpotential, internal resistance, mass-transfer limitation, or whether a practical cell will deliver the same terminal voltage under load.
When to use it
Use it when checking a laboratory redox calculation, comparing a reaction at two temperatures, estimating how a concentration or activity ratio shifts an electrode potential, or preparing a reproducible calculation for a report. The IUPAC definition of the Nernst equation explains the underlying relationship between equilibrium electrode potential and chemical activities.
How to calculate
- The calculator opens with a complete magnesium – lead-style demonstration: E° = 2.25 V, 25 °C, two electrons, reduced-form activity 0.02, and oxidized-form activity 0.20. Its result and a validated example Excel workbook are available immediately.
- Replace the values with data from your balanced reduction reaction. Keep the sign convention of the standard reduction potential consistent with the reaction as written.
- Select °C or K for Temperature. Changing the unit converts the current entry rather than merely relabeling it.
- Read Reduction potential (E) and the intermediate values. The breakdown table shows the temperature conversion, ratio, logarithm, thermal factor, and final substitution.
- Select Download Excel to create a current-state .xlsx workbook. Reset clears the demonstration values and results; Excel export remains disabled until every required field again contains a complete valid state.
Input guide
Standard reduction potential (E°) is a required signed decimal in volts, such as 2.25. It is the potential under the chosen standard-state convention. Raising E° raises E by exactly the same voltage. A frequent mistake is combining an oxidation potential with a reduction-form equation without reversing its sign.
Temperature is required and accepts an ordinary decimal in °C or K, such as 25 °C or 298.15 K. The absolute temperature must be above 0 K. Higher temperature magnifies the activity-dependent correction whenever the ratio differs from 1. Do not enter Fahrenheit, a unit symbol, or a comma-decimal value such as 25,5.
Electrons transferred (z) is a required positive whole number, for example 2. It comes from the balanced redox reaction, not from the number of ions in solution. A larger z reduces the magnitude of the Nernst correction. Fractional, zero, and negative electron counts are rejected.
Activity (reduced form) and Activity (oxidized form) are required positive dimensionless values, for example 0.02 and 0.20. Their ratio is the quantity inside the natural logarithm. Multiplying both by the same factor leaves the result unchanged. Zero and negative values are invalid because their logarithm is undefined. Using concentration in place of activity is an approximation whose quality declines as non-ideal interactions grow.
Output guide
Reduction potential (E) is the primary equilibrium result in volts. Activity ratio is reduced activity divided by oxidized activity. Natural logarithm is ln of that ratio. Thermal factor RT/zF expresses the voltage scale of the correction, and Nernst correction is the signed product (RT/zF)ln(ratio) that is subtracted from E°. A ratio of 1 gives ln(1) = 0, so E equals E°. A ratio below 1 produces a negative correction and raises E above E°; a ratio above 1 lowers E below E°.
Worked example
For the startup values, 25 °C converts to 298.15 K. The activity ratio is 0.02/0.20 = 0.1, and ln(0.1) = – 2.302585. Using R = 8.314462618 J·mol⁻¹·K⁻¹, F = 96485.33212 C·mol⁻¹, and z = 2 gives RT/zF = 0.0128463 V. The correction is 0.0128463 × – 2.302585 = – 0.029579 V. Therefore E = 2.25 – ( – 0.029579) = 2.2796 V, matching the first-open result.
Formula, assumptions, and interpretation
E = E° – (RT / zF) × ln(ared / aox)
The gas constant R converts temperature into an energy-per-mole scale, while the Faraday constant F converts energy per mole of electrons into volts. The quotient must match the reaction convention used for E°. This calculator follows the reduced-form to oxidized-form ratio shown in the interface and reports all intermediate signs explicitly.
The Chemistry LibreTexts treatment of the Nernst equation gives additional examples under non-standard conditions. For terminology and the role of activities, consult the IUPAC Gold Book definition of activity.
Common mistakes
- Using degrees Celsius directly in RT instead of converting to kelvins.
- Using the wrong electron count after balancing the oxidation and reduction half-reactions.
- Reversing the activity quotient without also changing the reaction convention.
- Treating concentration as exact activity in a strongly non-ideal solution.
- Interpreting equilibrium potential as a guaranteed operating voltage under current.