This Nernst equation calculator finds a half-cell or full-cell potential under non-standard conditions — from E°, electrons transferred n, temperature and the reaction quotient Q.
E = E° − (RT ÷ nF) · ln Q — Voltage With Conditions Attached
Standard potentials assume 1 M everything, 1 atm, pure phases — conditions no working battery maintains for long. Nernst adjusts: as products accumulate (Q grows), the potential sags logarithmically; dilute the products and it recovers. The equation also reads backwards in analytical chemistry: a pH electrode is a Nernst device (0.05916 V per pH unit at 25 °C is the same coefficient). Part of our Chemistry Calculators collection.
Worked Example (Verified)
- E° = 0.34 V, n = 2, Q = 0.01 at 25 °C (defaults): E = 0.34 − (0.05916/2)(−2) = 0.399 V — fresh, product-poor conditions beat standard by 59 mV
- Equilibrium limit: Q = K ⇒ E = 0 — and combining with ΔG° = −RT ln K gives log K = nE°/0.05916, the fastest route from a potentials table to an equilibrium constant
- Concentration cell: same electrodes, Q from a 100:1 concentration ratio, n=1 → E = 0.05916 × 2 = 0.118 V — voltage from nothing but inequality of concentrations
- Temperature matters mildly: at 37 °C (body) the decade coefficient is 0.0615 V — physiology's electrodes run a slightly hotter Nernst
Constructing Q Correctly
- Q = products over reactants, each raised to its stoichiometric power, using activities (≈ molarities for solutes, partial pressures for gases).
- Pure solids and liquids have activity 1 — they vanish from Q (metal electrodes and precipitates don't appear).
- n is the electrons in the balanced half/full reaction as written — double the reaction, double n and Q's powers together; E stays invariant, as an intensive quantity must.
- Sign conventions: E > 0 = spontaneous as written (galvanic); E < 0 = the reverse runs (or you built an electrolytic cell).
Related Tools
- Gibbs Free Energy Calculator — ΔG = −nFE's other half
- pH Calculator — the Nernstian glass electrode
- Chemistry Calculators — the full collection
Frequently Asked Questions
What is the Nernst equation?
E = E° − (RT/nF) ln Q — cell potential corrected for actual conditions. At 25 °C it simplifies to E = E° − (0.05916/n) log₁₀ Q. Inputs: standard potential, electrons transferred, reaction quotient, temperature. The defaults (0.34 V, n=2, Q=0.01) give 0.399 V.
Why does a battery's voltage drop as it discharges?
Discharge consumes reactants and accumulates products, so Q rises; the Nernst term −(RT/nF) ln Q grows more negative and E sags toward zero at equilibrium (Q = K). The discharge curve's shape is largely this logarithm, plus kinetic and resistance effects the equation doesn't model.
What is Q and how do I write it?
The reaction quotient: activities of products over reactants, each to its stoichiometric power, at the current (non-equilibrium) state. Solutes ≈ molarity, gases ≈ partial pressure in atm, pure solids/liquids = 1 (omitted). Q's value relative to 1 tells you which side conditions favor.
How does a pH meter use the Nernst equation?
The glass electrode develops a potential proportional to log[H⁺] across its membrane — a Nernst slope of 59.16 mV per pH unit at 25 °C (temperature-compensated in real meters, since the coefficient is RT/F-based). Calibration with two buffers fixes the electrode's E° drift.
Can E exceed E°?
Yes — whenever Q < 1 (reactants concentrated, products dilute), the correction term flips positive. "Standard" is a reference condition, not a maximum: fresh cells and concentrated reactants push above it, which the worked example shows (+59 mV at Q = 0.01, n = 2).
Is this Nernst equation calculator free?
Yes — free, instant, no sign-up.