# Nernst Equation Calculator

E = E⁰ − (RT/nF)·lnQ at any temperature, with the thermal factor RT/F, per-decade step 2.303RT/nF, and ΔG = −nFE.

> Canonical page: https://elysiatools.com/en/tools/nernst-equation-calculator

- **Category:** Science & Education

- **Keywords:** nernst equation, electrode potential, cell potential, reaction quotient, concentration cell, electrochemistry

## Overview

The Nernst Equation Calculator computes real cell and electrode potentials under non-standard conditions using the formula E = E⁰ − (RT/nF)·lnQ. By providing the standard potential, number of electrons transferred, reaction quotient, and temperature in Kelvin or Celsius, you instantly obtain the thermal factor RT/F, the Nernst correction term, the slope per decade of Q, the actual cell potential E, and the Gibbs free energy change ΔG.

## Inputs

- **Standard potential E⁰ (V)** (number): e.g. 1.10
- **Electrons transferred n** (number): e.g. 2
- **Reaction quotient Q** (number): e.g. 100
- **Temperature** (number): e.g. 298.15
- **T unit** (select)

## When to use

- Determining the non-standard voltage of an electrochemical or galvanic cell as reactants deplete and reaction quotient Q changes.
- Evaluating ion-selective electrode potentials, pH sensor responses, or concentration cells across temperature variations.
- Calculating the change in Gibbs free energy (ΔG = −nFE) for redox reactions at specified temperatures and concentrations.

## How it works

- Enter the standard electrode or cell potential E⁰ in volts and specify the number of electrons transferred (n).
- Provide the reaction quotient Q representing the ratio of product to reactant activities or concentrations.
- Input the operating temperature and select whether the value is in Kelvin (K) or Celsius (°C).
- Review the resulting cell potential E, thermal voltage RT/F, per-decade slope (2.303RT/nF), and Gibbs free energy ΔG.

## Use cases

- Analyzing galvanic battery discharge curves by tracking voltage drop as the reaction quotient Q increases.
- Calibrating potentiometric sensors and ion-selective electrodes using the theoretical millivolt response per decade of analyte activity.
- Solving electrochemistry homework and lab calculations involving non-standard redox systems and concentration gradients.

## Frequently asked questions

### What is the Nernst equation?

It is an electrochemical equation, E = E⁰ − (RT/nF)·lnQ, relating reduction potential to standard potential, temperature, electron count, and reaction quotient.

### What is the 59.16 mV rule?

At 25 °C (298.15 K), the term 2.303·RT/F equals 59.16 mV, meaning a single-electron transfer shifts potential by 59.16 mV per decade change in Q.

### How does temperature affect cell potential in this calculator?

Temperature scales the thermal voltage term RT/F, altering both the Nernst correction factor and the resulting Gibbs free energy ΔG.

### Can I input temperature in Celsius?

Yes, you can choose Celsius (°C) or Kelvin (K) from the unit selector, and the calculator automatically handles conversion to absolute temperature.

### How is Gibbs free energy calculated?

It is calculated using the relation ΔG = −nFE, where n is transferred electrons, F is the Faraday constant, and E is the calculated cell potential.

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