Daniell cell
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s); n = 2
Q = [Zn²⁺]/[Cu²⁺] = 0.10/1.00 = 0.10
E = 1.10 − (0.05916/2)log(0.10) = 1.130 V
Nernst Equation Calculator: Cell EMF, Q, and K
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.
Build reaction quotient Q
Add species from the balanced overall reaction. Values are converted to M or bar; pure solids and liquids are automatically omitted.
Generated expression: Add species to build Q.
Results
Primary result
-
Choose a mode and calculate.
Nernst terms
Coefficient RT/nF: -
log10 term: -
Temperature: -
Reaction values
n: -
Q or ratio: -
K: -
Interpretation
-
Step-by-step solution
Advertisement
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
Magnesium/lead cell
Mg(s) + Pb²⁺(aq) → Mg²⁺(aq) + Pb(s); n = 2
Q = [Mg²⁺]/[Pb²⁺] = 0.10/0.010 = 10
E = 2.24 − (0.05916/2)log(10) = 2.210 V
Find Q from measured EMF
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s); n = 2
log Q = n(E° − E)/0.05916 = 2(1.10 − 1.07)/0.05916
Q = 10.33
Estimate K from E°
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s); n = 2
log K = nE°/0.05916 = 2(1.10)/0.05916
K ≈ 1.65 × 10³⁷
Copper concentration cell
Cu²⁺(0.010 M) → Cu²⁺(1.00 M); n = 2
ratio = a_high/a_low = 1.00/0.010 = 100
E = (0.05916/2)log(100) = 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.
E, E°, reduction potential, and cell EMF
E° is the standard potential at standard-state activities (commonly 1 for dissolved species and gases) at the stated temperature; E is the actual potential at the current composition. A reduction potential describes one half-reaction written as a reduction. For a complete cell, E°cell = E°cathode − E°anode when both tabulated values are reduction potentials.
Cell EMF is the open-circuit voltage predicted for the overall reaction. A concentration-cell EMF comes from an activity difference even though both electrodes use the same redox couple. Enter a tabulated half-cell E° only in half-cell mode; in cell modes, enter the overall E°cell.
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.
Common mistakes
- Reversing the reaction without reversing the sign of E° or inverting Q.
- Using a half-reaction coefficient instead of the electrons canceled in the balanced overall reaction for n.
- Including pure solids or liquids in Q; their activities are 1.
- Treating concentration as exact activity in non-ideal solutions.
- Mixing the natural-log form RT/nF ln Q with the base-10 coefficient.
- Using 0.05916 V/n away from 25 °C.
Calculation basis
Constants: R = 8.314462618 J mol⁻¹ K⁻¹; F = 96485.33212 C mol⁻¹.
Conventions: IUPAC-style reduction potentials and dimensionless activities; pure solids and liquids have unit activity. The full natural-log equation is calculated first, while the 25 °C base-10 form is shown as a shortcut.
Rounding: calculations retain JavaScript floating-point precision; displayed voltages use up to six decimals and worked examples round to suitable significant figures. Last reviewed: 12 July 2026.
FAQ
How do I calculate Q?
Write activities of products over reactants, raise each to its balanced stoichiometric coefficient, and omit pure solids and liquids. The Q builder above performs these operations and unit conversions.
Why are solids and liquids omitted from Q?
A pure solid or liquid has activity defined as 1, so including it would not change the quotient.
How do I find n?
Balance the oxidation and reduction half-reactions, then use the number of electrons that cancel in the balanced overall reaction. Do not add the two electron counts.
What does a negative E mean?
The written forward reaction is nonspontaneous under the entered conditions. Reversing the reaction reverses the potential sign.
What is the 0.0592/n form?
At 25 °C, converting the natural logarithm to base 10 gives E = E° − (0.05916 V/n)log10(Q), often rounded to 0.0592.
When should I use activities instead of concentrations?
Use activities for thermodynamic accuracy, especially in concentrated or high-ionic-strength solutions. Concentrations are common approximations for dilute classroom problems.
Why does voltage change with temperature?
The correction coefficient is RT/nF, so temperature directly changes how strongly composition shifts the potential.
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.
When is Q equal to 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.
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.