Nernst Equation Calculator
Find the cell potential under non-standard conditions with the Nernst equation, E_cell = E°_cell − (0.0592/n)log₁₀(Q) at 25°C. Static 3D diagrams and charts show a two-electrode cell and how E_cell shifts with reaction quotient Q.
Reviewed by the ToolNestr Editorial Team — July 2026
Uses the simplified 25°C form: E_cell = E°_cell − (0.0592/n)log₁₀(Q).
Two ideas that trip students up
1. Two electrodes, ion flow, and electron flow
A fixed snapshot of a galvanic cell: two electrodes in separate half-cells, connected by a wire (electron flow) and a salt bridge (ion flow) that completes the circuit.
2. E_cell vs log(Q) — a straight line
Three fixed points on the E_cell-vs-log(Q) line for n = 2 — the slope is always −0.0592/n, regardless of E°_cell.
Nernst equation graphs
How it works
The core idea in one line: a cell's real voltage is its standard voltage, nudged up or down by how far the actual concentrations are from the standard 1 M reference point.
Ecell = E°cell − (0.0592/n) log₁₀(Q)
simplified form, valid at 25°C (298 K)
Ecell = E°cell − (RT/nF) ln(Q)
full form for any temperature — R=8.314 J/(mol·K), F=96,485 C/mol
Because the correction term is a logarithm of Q divided by n, every tenfold change in Q shifts E_cell by a fixed amount — 0.0592/n volts at 25°C. More electrons transferred (larger n) means each factor-of-ten change in Q has a smaller effect on the cell potential, since the correction is spread across more charge.
Worked example 1 — non-standard Daniell cell (Zn/Cu)
Given: A Zn/Cu galvanic cell has E°_cell = 1.10 V, n = 2 electrons transferred, and Q = 0.500 (non-standard concentrations). Find E_cell at 25°C.
E_cell ≈ 1.109 V, slightly higher than the standard 1.10 V, because Q < 1 favors the forward reaction a bit more than standard conditions.
Worked example 2 — effect of a larger reaction quotient
Given: Same Zn/Cu cell, E°_cell = 1.10 V, n = 2, but now Q = 10 (products/reactants ratio has grown). Find E_cell.
A larger Q (more product relative to reactant) lowers E_cell — consistent with the cell having less remaining driving force as it discharges toward equilibrium.
How E_cell shifts with Q, for a cell with E°_cell = 1.10 V, n = 2
Every tenfold change in Q shifts E_cell by exactly 0.0592/n volts — here, 0.0296 V per decade.
| Q | log₁₀(Q) | E_cell (V) |
|---|---|---|
| 0.01 | −2 | 1.1592 |
| 0.5 | −0.301 | 1.1089 |
| 1 (standard) | 0 | 1.1000 |
| 10 | 1 | 1.0704 |
| 100 | 2 | 1.0408 |
At Q = 1, E_cell = E°_cell exactly, since log₁₀(1) = 0 — the standard-condition reference point.
Where the Nernst equation actually matters
🔋 Battery voltage during discharge
As a battery discharges, reactant concentrations fall and product concentrations rise, pushing Q upward and E_cell downward — the Nernst equation explains why a battery's voltage sags gradually rather than staying perfectly flat until it suddenly dies.
🧠 Neuronal membrane potentials
The Nernst equation (in its ion-specific form) predicts the equilibrium potential for a single ion species across a cell membrane, such as K⁺ or Na⁺ — foundational to understanding how neurons generate and propagate electrical signals.
🧪 pH meters and ion-selective electrodes
pH meters work by measuring a voltage that depends on [H⁺] via a Nernst-equation relationship, translating that voltage into a pH reading — the same equation underlies many ion-selective electrode sensors.
⚙️ Corrosion and metal plating engineering
Engineers use Nernst-equation reasoning to predict which metal will corrode preferentially in a given environment, and to calculate the plating voltages needed for electroplating processes at non-standard ion concentrations.
Common misconceptions
"E°_cell and E_cell are always the same number."
E°_cell is the potential only under standard conditions (1 M concentrations, 1 atm gases, 25°C). E_cell is the actual potential under whatever real conditions exist, which the Nernst equation calculates by correcting E°_cell for how far Q is from 1.
"The 0.0592/n shortcut works at any temperature."
The 0.0592 V value comes from RT/F evaluated specifically at 298 K (25°C). At any other temperature, you must use the full form E_cell = E°_cell − (RT/nF)ln(Q) with the actual temperature in Kelvin.
"A bigger Q always means a bigger E_cell."
It's the opposite — because Q is subtracted (as a log term) from E°_cell, a larger Q lowers E_cell, and a smaller Q (less than 1) raises it above E°_cell. Larger Q means the reaction has moved further toward products, which reduces its remaining driving force.
"When E_cell = 0, the reaction has stopped completely."
E_cell = 0 means the cell has reached electrochemical equilibrium (Q = K) — no further net current flows, but this reflects a dynamic balance of forward and reverse electron transfer, not that all chemical activity has ceased.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — Chapter 17, Electrochemistry: the Nernst equation (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 20, Electrochemistry.
- • Zumdahl & Zumdahl, Chemistry — the Nernst equation and concentration cells.
E_cell = E°_cell − (0.0592/n)log₁₀(Q) at 25°C (298 K); full form E_cell = E°_cell − (RT/nF)ln(Q) for other temperatures. Results are rounded for display.
How to use this calculator
Enter E°_cell
The standard cell potential in volts, from a standard reduction potential table.
Enter n and Q
Electrons transferred in the balanced redox reaction, and the reaction quotient at actual conditions.
Read E_cell
The actual cell potential at 25°C solves live, with the 3D cell diagram and charts.
Related tools
Frequently asked questions
What does the Nernst equation calculate?
The Nernst equation gives the actual cell potential (E_cell) of an electrochemical cell under any set of concentrations, not just standard 1 M conditions. It corrects the standard cell potential E°_cell for how far the reaction quotient Q is from 1.
What is the simplified 0.0592/n form, and when can I use it?
The full Nernst equation is E_cell = E°_cell − (RT/nF)ln(Q). At exactly 25°C (298 K), substituting R = 8.314 J/(mol·K) and F = 96,485 C/mol and converting ln to log₁₀ simplifies RT/F to 0.0592 V, giving E_cell = E°_cell − (0.0592/n)log₁₀(Q). This shortcut only holds at 25°C — at other temperatures you need the full RT/nF form.
What is Q in the Nernst equation?
Q is the reaction quotient for the cell's overall redox reaction — the same expression as the equilibrium constant K, but evaluated at the actual (non-equilibrium) concentrations present in the cell right now, typically [products]/[reactants] raised to their stoichiometric coefficients.
What happens to E_cell as the cell approaches equilibrium?
As a cell discharges, Q moves toward K (the equilibrium constant), and E_cell drops toward zero. At equilibrium, Q = K and E_cell = 0 — a dead battery, in effect, since no further net electron flow is thermodynamically favored.
How is the Nernst equation used in real batteries?
It explains why a battery's voltage is not perfectly constant — it drops gradually as the cell discharges and concentrations shift, and it also underlies concentration cells and biological membrane potentials (like the Nernst potential for ion channels in neurons).