# Nernst Equation Calculator

URL: https://speedycalculator.com/calculators/chemistry/nernst-equation/
Last updated: 2026-10-30

> The Nernst equation calculator finds the actual potential of a half-cell or a whole cell under non-standard conditions from the standard potential, the number of electrons, the temperature and the activities (or the reaction quotient), with a table of real half-reactions to start from.

## Inputs

- Apply the Nernst equation to
- Half-reaction
- Standard reduction potential E° (V)
- Electrons transferred z
- Activity of the reduced form [red] — Metals and other pure solids: 1
- Activity of the oxidised form [ox] — Concentration in mol/L for dilute solutions
- Standard cell potential E°cell (V)
- Electrons transferred n
- Reaction quotient Q — Products over reactants, e.g. [Zn²⁺]/[Cu²⁺] for a Daniell cell
- Temperature (K, °C, °F)

## Results

- Standard potential used
- Electrons z
- ln of the quotient
- RT/(zF)
- Slope per tenfold change (2.303RT/zF)
- Potential E
- Shift from the standard potential
- Gibbs energy change ΔG = −zFE
- log₁₀K (equilibrium constant)

## Formula

```
Half-cell: E = E° − (RT/zF)·ln(a_red/a_ox) · Cell: E = E°cell − (RT/nF)·ln Q · at 25 °C: E = E° − (0.05916 V/n)·log₁₀Q
```

## Explanation

Standard potentials only describe one special case – every species at unit activity. Real batteries, corrosion cells, biological membranes and sensors work at other concentrations, and their voltage shifts accordingly. Walther Nernst derived the correction in 1889 from ΔG = ΔG° + RT ln Q combined with ΔG = −nFE: the potential falls by RT/(nF) for every factor of e that the reaction quotient increases.

At 25 °C the factor 2.303RT/F equals 59.16 mV, so a one-electron couple moves by 59 mV for every tenfold change in the activity ratio and a two-electron couple by about 29.6 mV. This is the principle behind the pH electrode (59 mV per pH unit), ion-selective electrodes, the resting potential of nerve cells and the gradual voltage drop of a discharging battery. When the cell reaches equilibrium, Q = K and E falls to zero.

Strictly the equation uses activities; for dilute solutions concentrations in mol/L (and partial pressures in bar for gases) are a good approximation. Pure solids and liquids such as metal electrodes and water have activity 1 and are left out of Q.

### How to use the Nernst Equation Calculator

- **Apply the Nernst equation to**
- **Half-reaction**
- **Standard reduction potential E°**
- **Electrons transferred z**
- **Activity of the reduced form [red]** — Metals and other pure solids: 1
- **Activity of the oxidised form [ox]** — Concentration in mol/L for dilute solutions
- **Standard cell potential E°cell**
- **Electrons transferred n**
- **Reaction quotient Q** — Products over reactants, e.g. [Zn²⁺]/[Cu²⁺] for a Daniell cell
- **Temperature**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose a single electrode (half-cell) or a whole cell. For a half-cell, pick a reduction half-reaction (or enter E° and z) and give the activities of the reduced and oxidised forms; for a cell, enter E°cell, n and the reaction quotient Q. The calculator evaluates RT/(zF) at your temperature and subtracts the correction from E°.

### Worked example

Copper electrode in 0.01 M Cu²⁺ at 25 °C: E = 0.3419 − (8.314 × 298.15 / (2 × 96 485)) × ln(1/0.01) = 0.3419 − 0.012846 × 4.6052 = **0.28274 V**, 59.2 mV below the standard value.

Daniell cell with [Zn²⁺] = 1 M and [Cu²⁺] = 0.1 M (Q = 10) at 25 °C: E = 1.1037 − 0.012846 × ln 10 = 1.1037 − 0.0296 = 1.0741 V.

### Nernst slope at common temperatures

Temperaturen = 1n = 2n = 30 °C54.20 mV27.10 mV18.07 mV20 °C58.17 mV29.08 mV19.39 mV25 °C59.16 mV29.58 mV19.72 mV37 °C61.54 mV30.77 mV20.51 mV50 °C64.12 mV32.06 mV21.37 mV100 °C74.04 mV37.02 mV24.68 mV

### Tips

- Standard potentials are reduction potentials at 25 °C, 1 M and 1 bar.
- n is the number of electrons transferred in the balanced reaction.
- Faraday constant: 96 485 C per mole of electrons.
- Everything is calculated in your browser.

### Common mistakes to avoid

- Flipping the sign of a potential and also subtracting it (counting the reversal twice).
- Multiplying a standard potential by the coefficient of the half-reaction – potentials are intensive.
- Using log base e where the Nernst equation uses log₁₀ (or the other way round).

### Inputs explained

FieldWhat to enterApply the Nernst equation toChoose one: A single electrode (half-cell reduction potential), A whole cell (cell potential from Q)Half-reactionChoose one: F₂ + 2e⁻ → 2F⁻ (E° = +2.866 V), H₂O₂ + 2H⁺ + 2e⁻ → 2H₂O (E° = +1.776 V), PbO₂ + SO₄²⁻ + 4H⁺ + 2e⁻ → PbSO₄ + 2H₂O (E° = +1.6913 V), MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O (E° = +1.507 V) …Standard reduction potential E°In VElectrons transferred zA numberActivity of the reduced form [red]A number. Metals and other pure solids: 1Activity of the oxidised form [ox]A number. Concentration in mol/L for dilute solutionsStandard cell potential E°cellIn VElectrons transferred nA numberReaction quotient QA number. Products over reactants, e.g. [Zn²⁺]/[Cu²⁺] for a Daniell cellTemperatureUnits: K, °C, °F

### What each result means

- **RT/(zF)** = 8.314462618×[Temperature]÷([Electrons z]×96485.33212)×1000
- **Slope per tenfold change (2.303RT/zF)** = [RT÷(zF)]×ln(10)
- **Potential E** = [Standard potential used] - [RT÷(zF)]÷1000×[ln of the quotient]
- **Shift from the standard potential** = ([Potential E] - [Standard potential used])×1000
- **Gibbs energy change ΔG = −zFE** = -[Electrons z]×96485.33212×[Potential E]÷1000
- **log₁₀K (equilibrium constant)** = [Electrons z]×[Standard potential used]×96485.33212÷(8.314462618×[Temperature]×ln(10))

## Worked example

Inputs — Apply the Nernst equation to: A single electrode (half-cell reduction potential); Half-reaction: Cu²⁺ + 2e⁻ → Cu (E° = +0.3419 V); Activity of the reduced form [red]: 1; Activity of the oxidised form [ox]: 0.01; Temperature: 298.15 K.

Results — Standard potential used = 0.3419 V; Electrons z = 2; ln of the quotient = 4.6052; RT/(zF) = 12.8463 mV; Slope per tenfold change (2.303RT/zF) = 29.58 mV/decade; **Potential E = 0.28274 V**; Shift from the standard potential = -59.16 mV.

## Key terms

- **Reaction quotient Q**: Product of product activities divided by product of reactant activities, each raised to its coefficient.
- **Activity**: Effective concentration; about c/(1 mol/L) for dilute solutes, 1 for pure solids and liquids.
- **Nernst slope**: 2.303RT/(nF), the potential change per tenfold change in Q.
- **Standard potential**: Potential when all activities equal 1.

## FAQ

**What is the Nernst equation?**
E = E° − (RT/nF)·ln Q. It corrects a standard potential for real concentrations (activities) and temperature.

**What is 0.0592 in the Nernst equation?**
2.303·RT/F at 25 °C (298.15 K) = 0.05916 V. It converts ln to log₁₀, giving E = E° − (0.05916/n)·log Q.

**What is the potential of a Cu electrode in 0.01 M Cu²⁺?**
E = 0.3419 − (0.05916/2)·log(1/0.01) = 0.3419 − 0.0592 = 0.2827 V.

**How does temperature affect the Nernst equation?**
The correction is proportional to the absolute temperature: at 37 °C the slope is 61.5 mV per decade for n = 1 instead of 59.2 mV at 25 °C.

**What happens when E = 0?**
The cell is at equilibrium, Q equals the equilibrium constant K, and no net current flows – a "dead" battery.

**Can I use concentrations instead of activities?**
For dilute solutions (below about 0.01 M) yes. At higher ionic strength, activity coefficients below 1 make the real activity noticeably smaller.

**How does the Nernst equation explain the pH electrode?**
For H⁺ the potential shifts by 59.16 mV per pH unit at 25 °C, so measuring the voltage gives the pH directly.

**What formula does the Nernst Equation Calculator use?**
Half-cell: E = E° − (RT/zF)·ln(a_red/a_ox) · Cell: E = E°cell − (RT/nF)·ln Q · at 25 °C: E = E° − (0.05916 V/n)·log₁₀Q.


## Sources

- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)
- [CRC Handbook of Chemistry and Physics – Electrochemical series](https://hbcp.chemnetbase.com/)
- [NIST – Fundamental physical constants (CODATA)](https://physics.nist.gov/cuu/Constants/)