Nernst Equation Calculator
A cell away from its standard state is a cell with a new voltage — E = E° − (RT/nF)·ln Q prices the drift in millivolts.
Nernst Equation Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- One redox couple — no mixed potentials
- Q as a plain number; activities and their coefficients belong to the typist
In short: A Daniell cell pushed off its standard state — E° 1.100000 V, two electrons exchanged, the reaction quotient at 0.1 — reads 1.129580 V: the quotient below one means the reaction ran forward, and the cell collects 29.580 mV of bonus potential for it. The exchange rate at 298.15 K is R·T·ln 10/F = 0.059159 V per electron per tenfold swing of Q — the fifty-nine millivolts every electrochemist carries. Type Q = 1 and the cell is back on its standard state: E = E° exactly.
Formula
E = E° − (R·T/nF)·ln Q · slope = R·T·ln 10/F = 0.059159 V at 298.15 K
The Nernst equation is the thermodynamic bill for running a redox reaction off its standard snapshot: the potential moves by the reaction’s free-energy slope, R·T per mole of electrons per natural-log unit of Q. Tenfold in Q costs 0.059159 volts per electron at 298.15 K — a number derived from constants the pages already own: R = k₁k₂ exact, F = N_A·e exact, both pinned in the current SI.
Worked Example
- Type the standard potential from your table.
- Type the electron count n and the temperature in Kelvin.
- Type the reaction quotient — the concentration or pressure ratio, products over reactants.
- Read the potential, the per-decade slope and the Q = 1 door.
Defaults: E° 1.1 V, n 2, 298.15 K, Q 0.1 → 1.129580 V. Tenfold harder: Q 0.01 → 1.159159 V. At body temperature the slope card reads 0.061540 V per decade per electron.
Strengths & Limits Of This Model
Where this engine is strong
- Slope derived from exact constants, not quoted
- The Q = 1 standard-state door printed
Where it stops
- No activity coefficients
- No liquid-junction or overpotential terms
Practical Use Cases
Electrochemistry bench
cell potentials off standard state
Membrane physiology
the Nernst slope per decade
Teaching
thermodynamics into volts
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Nernst Equation Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Where does the fifty-nine millivolt figure come from?
From constants, not a table: R·T·ln 10 divided by F at 298.15 K computes 0.059159 V. The gas constant is exact in the current SI, Faraday’s constant is N_A times e with both fixed, and 298.15 K is the 25 °C convention. At body temperature the same formula gives 0.061540 V — the slope is a thermometer reading, not a constant of nature.
Why does Q = 1 return exactly E°?
Because the logarithm of one is zero and the whole correction vanishes — the standard state is by definition the snapshot where activities are one. The page prints it as a door rather than a number so the special case reads as physics, not coincidence.
Why is Q refused at zero?
A quotient of zero has no logarithm: the reaction as typed contains no products at all, which for a real cell is the start of a run, not a standing state. Type the smallest activity you can defend — or the moment before mixing, which no equation of state covers.
What sign convention does the page use?
E = E° − (RT/nF)·ln Q with Q as products over reactants: Q below one lifts E above E° (the reaction wants to run), Q above one drags it down. If your drive comes out backwards, the quotient is usually inverted — check that reactants sit in the denominator before blaming the arithmetic.
Can n be fractional?
Yes, and honestly so: averaged electron counts appear when a reaction is written with fractional stoichiometry or when coupled half-reactions are lumped. The slope divides by whatever n you type; the guard only refuses zero or negative lots of electrons.
Why is the slope card derived rather than quoted?
Because every constant in it is exact: R is pinned from k₁ and k₂, F from N_A and e, and the only table entry left is the temperature you typed. R·T·ln 10/F at 298.15 K computes 0.059159 V on the page — the fifty-nine millivolts stop being folklore and become arithmetic you can re-derive at any temperature, including the 0.061540 V body-heat value.
What does a negative drift mean?
That the quotient sits above one — products piled up past the standard snapshot — and the cell reads below E°. The sign is information: the reaction still runs forward but the return has shrunk. Push Q far enough and E crosses zero, the potential where the reaction loses its voluntary character; the page prints the millivolts either way.
How is this different from the pH pages?
Same mathematics, different rail. The pH pages run the minus-logarithm on one ion’s concentration with the water constant pinned; the Nernst page runs it on a whole reaction’s quotient with Faraday’s constant in the denominator. Both charge about sixty millivolts per decade at room temperature — the same thermodynamic tax.