Nernst Equation Calculator
Get cell potential from E0, temperature, electrons, and Q.
What it does
Batteries rarely run at standard conditions. Concentrations drift as current flows, temperature moves with the room, and the voltage follows. The Nernst equation tracks that follow with one compact rule linking potential to the reaction quotient and temperature.
The tool above applies the rule directly. Enter E0, Celsius temperature, electron count, and Q. It returns cell potential, the millivolt slope per tenfold Q shift, and kelvin for the record. Defaults describe a copper style cell (E0 = 0.34 V, n = 2) at 25 C with Q = 0.1, so the page opens solved at 0.3696 V.
Direction reads off Q at a glance. Quotient below 1 means reactants dominate, which lifts E above E0; above 1 means products dominate, which pulls E down. The worked example shows the lift: ln(0.1) is negative, minus a negative adds, and 0.34 V becomes 0.3696 V with a 29.58 mV slope.
Temperature enters through RT/nF, so warmer cells swing harder per decade. At 25 C the famous 59.16 mV per decade belongs to n = 1; halving to n = 2 gives 29.58 mV. The zinc copper practice case shows scale: E0 = 1.10 V with Q = 39 still holds 1.0529 V because the log term stays modest.
Use the table for decade landmarks, then run your cell. The page assumes ideal activity and a reversible setup; liquid junctions, internal resistance, and slow kinetics move real terminals. Within range it answers the bench question fast: what voltage should this mixture show right now.
How to use
- Enter standard potential E0 in volts.
- Enter temperature in Celsius.
- Enter electron count n.
- Enter reaction quotient Q above 0.
- Read cell potential, slope, and kelvin.
- Compare Q against 1 to see the shift direction.
Formula
- E0
- Standard potential in volts.
- T
- Cell temperature in C, converted to kelvin inside.
- n
- Electrons transferred, 1 to 10.
- Q
- Reaction quotient, products over reactants.
- R
- Gas constant 8.314 J/mol/K.
- F
- Faraday constant 96485 C/mol.
R is 8.314 J/mol/K, F is 96485 C/mol, T is kelvin, n counts electrons, and Q is the reaction quotient. The log10 form with 0.0592 V holds at 298.15 K only; the tool always uses the general ln form with your Celsius input converted inside.
Worked example
Example: copper cell at Q = 0.1
A copper half cell has E0 = 0.34 V with n = 2 at 25 C and Q = 0.1. Find the cell potential.
- Convert: T = 25 + 273.15 = 298.15 K.
- RT/nF = 8.314 x 298.15 / (2 x 96485) = 0.0128465 V.
- ln(0.1) = -2.302585.
- E = 0.34 - 0.0128465 x (-2.302585) = 0.34 + 0.02958 = 0.3696 V.
- Slope = 29.58 mV per tenfold Q at this n and T.
- Products favored below 1 in Q raise E above E0.
Reference table
| Q | n = 1 shift | n = 2 shift |
|---|---|---|
| 0.01 | +118.31 mV | +59.16 mV |
| 0.1 | +59.16 mV | +29.58 mV |
| 1 | 0 mV | 0 mV |
| 10 | -59.16 mV | -29.58 mV |
| 100 | -118.31 mV | -59.16 mV |
Limits
- Ideal activity; concentrated cells deviate.
- Reversible cells only; kinetics ignored.
- No junction potentials or resistance.
- Single temperature per run.
Common mistakes
- Using log10 with the ln constant.
- Entering Q as K without checking direction.
- Forgetting Celsius to kelvin inside.
- Mixing up n with stoichiometric sums.
- Expecting loaded terminal voltage here.
Try it yourself
Quick checks. Answers sit tucked under each question.
Zinc copper: E0 1.10 V, n = 2, Q = 39 at 25 C?
E = 1.0529 V. Slope 29.58 mV per decade. T = 298.15 K.
E0 0 V, n = 1, Q = 10 at 25 C?
E = -0.0592 V. Slope 59.16 mV per decade.
E0 0.34 V, n = 2, Q = 4 at 25 C? Work it by hand.
ln(4) = 1.3863. RT/F at 298.15 K = 0.02569 V. E = 0.34 - 0.02569 x 1.3863 / 1? No: with n = 2, E = 0.34 - 0.01285 x 1.3863 = 0.3222 V.
Questions
What is the Nernst equation?
The nonstandard cell potential rule: E = E0 - (RT/nF) ln Q. It shifts standard potential by concentration and temperature.
What is Q?
Reaction quotient: products over reactants raised to powers. Below 1 it lifts E above E0; above 1 it drags E down.
What is the slope per decade?
2.303 x RT/nF per tenfold Q. At 25 C with n = 2 that is 29.58 mV; with n = 1 it is 59.16 mV.
Do I enter Celsius or Kelvin?
Yes. Enter 25 C and the tool uses 298.15 K inside. Warmer cells shift the slope up with T.
How does it link to equilibrium?
At equilibrium Q = K and E = 0, so E0 predicts K: log K = nE0 / 0.0592 at 25 C.
Does it model real battery drain?
No. It assumes ideal activity, one temperature, and a reversible cell. Junctions, resistance, and kinetics sit outside.