The Nernst equation under nonstandard conditions
The Nernst equation relates an electrochemical cell’s ideal potential to its standard potential and reaction quotient. It accounts thermodynamically for composition and temperature but not for kinetic or electrical losses.
Reaction quotient Q must be dimensionless and consistent with the balanced overall reaction. Activities of pure solids and pure liquids are one and are omitted; electrons are not included in Q.
How to use the Nernst equation calculator
- Balance the redox reaction: Determine electron number n and preserve the chosen reaction direction.
- Enter standard potential: Use E° for that same balanced reaction direction.
- Build Q correctly: Use dimensionless activities raised to stoichiometric powers, omitting pure solids, pure liquids, and electrons.
- Enter kelvins: Provide positive absolute temperature and calculate the ideal nonstandard potential.
Formula and variables
The calculator uses R = 8.314462618 J/(mol·K), F = 96485.33212 C/mol, temperature in kelvins, and the natural logarithm.
E = E° − (RT/nF) ln Q- E — Nonstandard cell potential
- Ideal potential for the entered conditions (V)
- E° — Standard cell potential
- Potential for the reaction as written under standard-state conditions (V)
- T — Temperature
- Absolute thermodynamic temperature (K)
- n — Electron stoichiometric number
- Electrons transferred in the balanced reaction as written (dimensionless)
- Q — Reaction quotient
- Dimensionless activity quotient for the reaction as written (dimensionless)
Cell with Q below one
A two-electron reaction has E° = 1.10 V, T = 298.15 K, and Q = 0.01.
- E°
- 1.10 V
- T
- 298.15 K
- n
- 2
- Q
- 0.01
- E = 1.10 − [RT/(2F)] ln(0.01)
Result: The ideal nonstandard potential is approximately 1.15916 V.
Because Q is below one, ln Q is negative and the correction raises E above E° for the reaction as written.
Understanding your results
Potential follows reaction direction and quotient
At Q = 1, ln Q = 0 and E equals E°. At equilibrium, E = 0 for the balanced reaction under the stated convention.
- Q < 1 raises E relative to E° for the reaction as written.
- Q > 1 lowers E relative to E°.
- Reversing the reaction reverses E and replaces Q with 1/Q.
- Measured terminal voltage can differ because of resistance, overpotential, transport, and nonideal activity.
Assumptions
- Temperature is uniform and expressed in kelvins.
- E°, n, and Q refer to the same balanced reaction direction and scaling.
- Activities or justified dimensionless activity approximations are available.
Limitations
- Does not construct Q from concentrations or pressures.
- Does not calculate activity coefficients, junction potentials, overpotential, internal resistance, or loaded battery voltage.
- Concentration substitution can be inaccurate in nonideal or concentrated systems.
Common mistakes
- Using Celsius instead of kelvins.
- Using log10 with the natural-log coefficient RT/nF.
- Including pure solids, pure liquids, or electrons in Q.
- Using n from an unbalanced half-reaction or reversing E° without reversing Q.
Practical use cases
Electrochemistry coursework
Check nonstandard cell-potential calculations after balancing a redox reaction.
Condition sensitivity
Explore the ideal thermodynamic effect of Q and temperature on potential.
Frequently asked questions
Should I use ln or log10?
This calculator uses the natural logarithm with RT/nF. The common-log form requires the corresponding 2.303 factor.
What belongs in Q?
Use dimensionless activities of reaction species raised to stoichiometric powers; omit pure solids, pure liquids, and electrons.
Why is this different from the Cell Potential Calculator?
Cell Potential calculates E° from standard reduction potentials; this page adjusts an established E° for nonstandard thermodynamic conditions.
Sources and review
- Potential, Free Energy, and Equilibrium — OpenStax Chemistry 2e. Accessed 2026-07-13.
- Key Equations: Electrochemistry — OpenStax Chemistry. Accessed 2026-07-13.
Reviewed 2026-07-13.