Voltage tracks chemistry
The Nernst equation connects cell voltage directly to composition, so changing concentrations can shift a measurable electrical signal without changing the electrodes.
Nernst Equation / Cell EMF Calculator
Inputs
Use the balanced overall cell reaction.
Q must be positive and dimensionless.
Use the general Nernst equation E = E° - (RT/nF) ln(Q). Enter a positive, dimensionless reaction quotient for the balanced overall cell reaction.
Results
Primary result
-
Choose a mode and calculate.
Nernst terms
Coefficient RT/nF: -
log10 term: -
Temperature: -
Reaction values
n: -
Q or ratio: -
K: -
Interpretation
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Formula summary
| Quantity | Formula | Meaning |
|---|---|---|
| General Nernst equation | E = E° - (RT/nF) ln(Q) | Cell potential under non-standard conditions. |
| 25 °C form | E = E° - (0.05916 V / n) log10(Q) | Convenient base-10 form at 298.15 K. |
| Equilibrium relation | ln(K) = nFE° / RT | At equilibrium, E = 0 and Q = K. |
| Concentration cell | E = (RT/nF) ln(a_high / a_low) | Same redox couple with different activities or concentrations. |
This page uses R = 8.314462618 J mol⁻¹ K⁻¹ and F = 96485.33212 C mol⁻¹. For classroom-style calculations, concentrations or partial pressures can be used as activity proxies. Pure solids and pure liquids are omitted from Q.
Worked examples
| Case | Inputs | Result |
|---|---|---|
| Daniell cell | E° = 1.10 V, n = 2, Q = 0.100, 25 °C | E ≈ 1.130 V |
| Solve for Q | E° = 1.10 V, E = 1.07 V, n = 2, 25 °C | Q ≈ 10.33 |
| Equilibrium constant | E° = 0.763 V, n = 2, 25 °C | K ≈ 6.23 × 10²⁵ |
| Concentration cell | n = 2, a_high / a_low = 1.0 / 0.0100, 25 °C | E ≈ 0.05916 V |
The sign and size of the result depend on the balanced reaction direction, the number of electrons transferred, and whether Q is less than, equal to, or greater than 1.
How this Nernst calculator works
The main calculation uses the full temperature-dependent Nernst equation, so it works away from 25 °C. The page also reports the familiar base-10 logarithm term to make textbook checks easier and to show how strongly the quotient shifts the cell voltage.
This tool is intended for electrochemistry study, quick lab planning, and sanity checks. It does not infer balanced half-reactions, activity coefficients, salt-bridge effects, junction potentials, or kinetics. You must supply the correct n, reaction direction, and quotient definition for your system.
E = E° - (RT/nF) ln(Q)E = E° - (0.05916/n) log10(Q)ln(K) = nFE° / RTEconc = (RT/nF) ln(a_high / a_low)
Assumptions and limits
- Balanced reaction required: the calculator does not balance redox equations for you, so an incorrect n gives an incorrect result.
- Q is dimensionless: enter the quotient built from activities, or an accepted concentration or partial-pressure approximation.
- Standard states matter: pure solids and pure liquids do not appear in Q because their activities are taken as 1.
- High-accuracy work: for analytical or research-grade electrochemistry, formal potentials and activity corrections may be more appropriate than plain concentrations.
5 Fun Facts about the Nernst Equation
59.16 mV is a 25 °C shortcut
The well-known 0.05916 V coefficient comes from plugging constants into the equation at 298.15 K. At other temperatures, the factor changes.
Equilibrium means zero driving voltage
When a cell reaches equilibrium, the thermodynamic cell potential becomes zero and the quotient equals the equilibrium constant.
Concentration cells need no different metals
A concentration cell can produce a voltage using the same redox couple on both sides, as long as the activities or concentrations differ.
pH meters depend on the same idea
Many electrochemical sensors, including pH electrodes, rely on Nernst-style logarithmic voltage responses to chemical activity.
FAQ
Why does the cell potential drop when Q increases?
For a galvanic reaction written in the spontaneous forward direction, increasing product-heavy Q makes the logarithmic correction more positive, so the subtraction term gets larger and E falls.
What happens when Q equals K?
At equilibrium, the cell has no net driving force and the thermodynamic cell potential is 0 V. In that special case, the Nernst equation reduces to the equilibrium relation between K and E°.
Can this page replace a full electrochemistry model?
No. It handles the thermodynamic voltage relationship only. It does not account for overpotential, internal resistance, ionic strength corrections, or transport limitations.
Is any data stored or transmitted?
No. The page runs entirely client-side and does not upload your values.
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Electrochemistry note
This page is a calculation aid, not a substitute for a validated electrochemical method. It does not correct for activity coefficients, liquid-junction potentials, real-cell losses, or measurement uncertainty. Check your balanced reaction, standard potential reference, temperature, and state assumptions before using the result in lab work or engineering decisions.