Nernst Equation Calculator

Calculate the actual cell potential E from the standard potential E°, electrons transferred n, reaction quotient Q, and temperature using the Nernst equation.

🔋 Nernst Equation Calculator
V
K
Cell Potential (E)
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🔋 What is the Nernst Equation?

The Nernst equation, E = E° - (RT/nF) ln(Q), calculates the actual voltage (cell potential) of an electrochemical cell under any set of conditions, correcting the standard cell potential E° for the real reaction quotient Q, temperature T, and the number of electrons n transferred in the reaction. Named after chemist Walther Nernst, it is the bridge between tabulated standard electrode potentials (measured only under standard conditions) and the actual behaviour of real batteries, sensors, and biological membranes.

This equation shows up across chemistry and biology: predicting how a battery's voltage drops as it discharges and its reactants are consumed, calculating the reading of an ion-selective electrode like a pH probe, explaining why concentration cells generate voltage purely from a concentration difference with no chemical reaction at all, and computing the resting membrane potential of a neuron from ion concentration gradients across the cell membrane.

A common misconception is that the Nernst equation only works at 25°C using the familiar 0.0592/n shortcut taught in many introductory courses. That shortcut is a special case, valid only at 298.15 K; the full RT/nF form used by this calculator works at any temperature, which matters for biological systems (37°C body temperature) or industrial processes running well above or below room temperature.

This calculator applies the full Nernst equation directly, so you get an accurate cell potential at any temperature and instantly see how E changes as Q moves away from 1 on the accompanying chart.

📐 Formula

E  =  E° − (RT ÷ nF) × ln(Q)
E = actual cell potential, in volts (V)
E° = standard cell potential, in volts (V)
R = gas constant = 8.314 J/(mol·K)
T = absolute temperature, in kelvin (K)
n = number of electrons transferred (whole number)
F = Faraday constant = 96,485 C/mol
Q = reaction quotient (dimensionless)
At 25°C: simplifies to E = E° − (0.0592 ÷ n) × log₁₀(Q)

📖 How to Use This Calculator

Steps

1
Enter the standard cell potential - enter E°, the standard potential of the cell in volts, from a reference table or a prior calculation.
2
Enter electrons transferred and the reaction quotient - enter n, the whole number of electrons transferred, and Q, the reaction quotient under current conditions.
3
Enter the temperature - enter T in kelvin; use 298.15 K for standard room-temperature conditions.
4
Click Calculate to see the actual cell potential E, the substituted formula, and the E vs log(Q) chart.

💡 Example Calculations

Example 1 — Zinc-copper galvanic cell

E° = 1.10 V, n = 2, Q = [Zn²⁺]/[Cu²⁺] = 0.001, T = 298.15 K.

1
RT/nF = (8.314 × 298.15) / (2 × 96485) = 0.01285 V
2
E = 1.10 − 0.01285 × ln(0.001) = 1.1887 V
The dilute Zn²⁺ concentration raises the cell potential above the standard 1.10 V.
Try this example →

Example 2 — Products in excess

E° = 0.34 V, n = 2, Q = 10, T = 298.15 K.

1
RT/nF = (8.314 × 298.15) / (2 × 96485) = 0.01285 V
2
E = 0.34 − 0.01285 × ln(10) = 0.3104 V
With products in excess (Q > 1), the cell potential drops below the standard 0.34 V.
Try this example →

Example 3 — Body-temperature electrode

E° = 0.80 V, n = 1, Q = 0.5, T = 310 K (37°C, body temperature).

1
RT/nF = (8.314 × 310) / (1 × 96485) = 0.02671 V
2
E = 0.80 − 0.02671 × ln(0.5) = 0.8185 V
At body temperature, the correction term is larger than it would be at 25°C for the same n.
Try this example →

Example 4 — Negative standard potential with excess product

E° = −0.44 V, n = 2, Q = 100, T = 298.15 K.

1
RT/nF = (8.314 × 298.15) / (2 × 96485) = 0.01285 V
2
E = −0.44 − 0.01285 × ln(100) = −0.4992 V
Starting from a negative E°, a large Q pushes the potential even further negative.
Try this example →

❓ Frequently Asked Questions

What is the Nernst equation?+
The Nernst equation, E = E° - (RT/nF) ln(Q), relates the actual cell potential E of an electrochemical cell to its standard potential E°, adjusted for the current reaction conditions. R is the gas constant (8.314 J/(mol·K)), T is absolute temperature, n is the number of electrons transferred, F is the Faraday constant (96,485 C/mol), and Q is the reaction quotient describing how far the system is from standard-state concentrations.
What is the reaction quotient Q in the Nernst equation?+
Q has the same algebraic form as the equilibrium constant expression, products over reactants each raised to their stoichiometric coefficients, but uses the actual current concentrations or partial pressures rather than equilibrium values. Q = 1 when all species are at standard-state (1 M, 1 atm) conditions, which makes E = E° exactly, since ln(1) = 0.
What is the simplified 25°C form of the Nernst equation?+
At exactly 25°C (298.15 K), substituting R, F, and converting natural log to base-10 log gives E = E° - (0.0592/n) log10(Q), a common shortcut in introductory chemistry. This calculator uses the full temperature-dependent form, so at T = 298.15 K its answer matches the 0.0592/n shortcut to within rounding, and remains accurate at any other temperature where the shortcut would not apply.
Why does the Nernst equation include temperature?+
Cell potential depends on temperature because the thermodynamic driving force of a reaction (its Gibbs free energy) is itself temperature-dependent, and E is directly related to Gibbs free energy through ΔG = -nFE. Higher temperature increases the RT/nF term, making the reaction quotient's deviation from standard conditions matter proportionally more.
What does a negative cell potential mean?+
A negative E means the reaction, as written with the given concentrations, is non-spontaneous, the reverse reaction is thermodynamically favoured instead. This commonly happens when Q is far above 1 (products in large excess relative to reactants) even if the standard potential E° for the forward reaction is positive.
How do you find n, the number of electrons transferred?+
n comes directly from the balanced half-reaction or overall redox equation, it is the number of electrons that appear in the balanced electron-transfer step. For Zn²⁺ + 2e⁻ → Zn, n = 2. For Fe³⁺ + e⁻ → Fe²⁺, n = 1. Getting n wrong is one of the most common Nernst equation mistakes, since it directly scales the correction term.
What is the difference between E° and E in the Nernst equation?+
E° (standard cell potential) is a fixed reference value measured under standard-state conditions (1 M concentrations, 1 atm partial pressures, 25°C), tabulated for countless half-reactions. E (cell potential, sometimes written Ecell) is the actual potential under whatever real conditions are specified, which the Nernst equation calculates by correcting E° for how far Q is from 1.
Can the Nernst equation be used for concentration cells?+
Yes, and it is one of its most elegant applications. A concentration cell has identical electrodes with E° = 0 (since both half-reactions are the same reaction, just at different concentrations), so the entire cell potential comes purely from the Nernst equation's Q term, driven only by the concentration difference between the two half-cells, for example in the pH-sensing glass electrode.
How is the Nernst equation used in biology?+
The Nernst equation, applied to a single ion species, calculates the equilibrium (reversal) potential across a cell membrane, the membrane voltage at which an ion's electrical and concentration gradients exactly balance. This is fundamental to neuroscience and physiology for understanding resting membrane potential and action potentials, where potassium, sodium, and other ion gradients each have their own Nernst potential.
What happens to E as Q approaches the equilibrium constant K?+
As a reaction proceeds and Q approaches the equilibrium constant K, the cell potential E approaches zero, since at equilibrium there is no further net driving force (ΔG = 0, and ΔG = -nFE). This is why a battery's voltage gradually drops toward zero as it discharges: the reaction is progressing toward equilibrium, shifting Q toward K.
Does the sign convention of E and Q matter?+
Yes. E and Q must be defined consistently with the same overall cell reaction written in the same direction (reduction at the cathode, oxidation at the anode, as written). Flipping the reaction direction flips the sign of E° and inverts Q, and mixing conventions from different sources is a common source of sign errors in Nernst equation calculations.
Tags: Nernst Equation Calculator Cell Potential Calculator Electrochemistry Calculator Reaction Quotient Standard Electrode Potential Chemistry Calculator Free Online

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What is the Nernst equation?

The Nernst equation, E = E° - (RT/nF) ln(Q), relates the actual cell potential E of an electrochemical cell to its standard potential E°, adjusted for the current reaction conditions. R is the gas constant (8.314 J/(mol·K)), T is absolute temperature, n is the number of electrons transferred, F is the Faraday constant (96,485 C/mol), and Q is the reaction quotient describing how far the system is from standard-state concentrations.

What is the reaction quotient Q in the Nernst equation?

Q has the same algebraic form as the equilibrium constant expression, products over reactants each raised to their stoichiometric coefficients, but uses the actual current concentrations or partial pressures rather than equilibrium values. Q = 1 when all species are at standard-state (1 M, 1 atm) conditions, which makes E = E° exactly, since ln(1) = 0.

What is the simplified 25°C form of the Nernst equation?

At exactly 25°C (298.15 K), substituting R, F, and converting natural log to base-10 log gives E = E° - (0.0592/n) log10(Q), a common shortcut in introductory chemistry. This calculator uses the full temperature-dependent form, so at T = 298.15 K its answer matches the 0.0592/n shortcut to within rounding, and remains accurate at any other temperature where the shortcut would not apply.

Why does the Nernst equation include temperature?

Cell potential depends on temperature because the thermodynamic driving force of a reaction (its Gibbs free energy) is itself temperature-dependent, and E is directly related to Gibbs free energy through ΔG = -nFE. Higher temperature increases the RT/nF term, making the reaction quotient's deviation from standard conditions matter proportionally more.

What does a negative cell potential mean?

A negative E means the reaction, as written with the given concentrations, is non-spontaneous, the reverse reaction is thermodynamically favoured instead. This commonly happens when Q is far above 1 (products in large excess relative to reactants) even if the standard potential E° for the forward reaction is positive.

How do you find n, the number of electrons transferred?

n comes directly from the balanced half-reaction or overall redox equation, it is the number of electrons that appear in the balanced electron-transfer step. For Zn²⁺ + 2e⁻ → Zn, n = 2. For Fe³⁺ + e⁻ → Fe²⁺, n = 1. Getting n wrong is one of the most common Nernst equation mistakes, since it directly scales the correction term.

What is the difference between E° and E in the Nernst equation?

E° (standard cell potential) is a fixed reference value measured under standard-state conditions (1 M concentrations, 1 atm partial pressures, 25°C), tabulated for countless half-reactions. E (cell potential, sometimes written Ecell) is the actual potential under whatever real conditions are specified, which the Nernst equation calculates by correcting E° for how far Q is from 1.

Can the Nernst equation be used for concentration cells?

Yes, and it is one of its most elegant applications. A concentration cell has identical electrodes with E° = 0 (since both half-reactions are the same reaction, just at different concentrations), so the entire cell potential comes purely from the Nernst equation's Q term, driven only by the concentration difference between the two half-cells, for example in the pH-sensing glass electrode.

How is the Nernst equation used in biology?

The Nernst equation, applied to a single ion species, calculates the equilibrium (reversal) potential across a cell membrane, the membrane voltage at which an ion's electrical and concentration gradients exactly balance. This is fundamental to neuroscience and physiology for understanding resting membrane potential and action potentials, where potassium, sodium, and other ion gradients each have their own Nernst potential.

What happens to E as Q approaches the equilibrium constant K?

As a reaction proceeds and Q approaches the equilibrium constant K, the cell potential E approaches zero, since at equilibrium there is no further net driving force (ΔG = 0, and ΔG = -nFE). This is why a battery's voltage gradually drops toward zero as it discharges: the reaction is progressing toward equilibrium, shifting Q toward K.

Does the sign convention of E and Q matter?

Yes. E and Q must be defined consistently with the same overall cell reaction written in the same direction (reduction at the cathode, oxidation at the anode, as written). Flipping the reaction direction flips the sign of E° and inverts Q, and mixing conventions from different sources is a common source of sign errors in Nernst equation calculations.

📌 Quick Tips

💡n must be a whole number, the number of electrons transferred in the balanced half-reaction, e.g. n = 2 for Zn²⁺ + 2e⁻ → Zn.
💡Q is the reaction quotient, written the same way as an equilibrium constant expression but using current (not equilibrium) concentrations or pressures.
💡At 25°C (298.15 K), this reduces to the familiar shortcut E = E° - (0.0592/n) log10(Q), which this calculator's full form matches closely.
💡A negative E means the reaction as written is non-spontaneous under the given conditions, the reverse reaction is favoured instead.
💡Temperature must be in kelvin. The Nernst equation is genuinely temperature-dependent, unlike some simplified textbook shortcuts that fix T at 298.15 K.