The Nernst equation calculator is a five-in-one electrochemistry tool that solves the full Nernst expression for any one unknown given the other four. Whether you need the actual cell potential when concentrations deviate from 1 mol/L, want to back-calculate the standard reduction potential from a measured voltage, or need the temperature at which a cell reaches equilibrium, this calculator handles all five modes with step-by-step working, physical-constant precision and instant Gibbs free energy output. It is built for A-level and undergraduate chemistry, lab work and electrochemical engineering estimates.
How it works
The general Nernst equation is:
E = E° − (RT / nF) × ln(Q)
where E is the non-standard cell potential (V), E° is the standard cell potential at 25 °C and 1 mol/L (V), R = 8.314 J mol⁻¹ K⁻¹ is the universal gas constant, T is the absolute temperature in Kelvin, n is the moles of electrons transferred per formula unit of the balanced redox equation, F = 96 485 C mol⁻¹ is Faraday’s constant, and Q is the reaction quotient — the ratio of product activities to reactant activities at the moment of interest.
At 25 °C (298.15 K), the thermal prefactor RT/F equals 0.025693 V, giving the widely quoted 0.05916/n version when log₁₀ replaces ln (since ln = log₁₀ × 2.3026). The calculator always applies the exact form so results are correct at any temperature.
The tool also derives two further quantities automatically. First, Gibbs free energy: ΔG = −nFE. A positive E means ΔG < 0, confirming a spontaneous process. Second, the equilibrium constant K from ln(K) = nFE°/RT — K is independent of Q and tells you where the reaction would end up if left to reach equilibrium.
Worked example
A Daniell cell pairs a zinc anode (Zn → Zn²⁺ + 2e⁻) with a copper cathode (Cu²⁺ + 2e⁻ → Cu). Standard values: E°(Cu) = +0.34 V, E°(Zn) = −0.76 V, so E°(cell) = 0.34 − (−0.76) = +1.10 V.
Under standard conditions (Q = 1) E = E°. Now suppose [Zn²⁺] = 2.0 mol/L and [Cu²⁺] = 0.010 mol/L, giving Q = [Zn²⁺]/[Cu²⁺] = 200. At 25 °C (n = 2):
E = 1.10 − (0.025693 / 2) × ln(200)
E = 1.10 − 0.012847 × 5.298
E = 1.10 − 0.0681 = 1.032 V
The 200-fold concentration ratio lowers the cell potential by about 68 mV.
| Condition | Q | E (V) | Spontaneous? |
|---|---|---|---|
| Standard (1 M each) | 1 | 1.100 | Yes |
| [Cu²⁺] = 0.01 M | 100 | 1.041 | Yes |
| [Cu²⁺] = 0.001 M | 1 000 | 1.012 | Yes |
| Q = K (equilibrium) | ~1.7×10³⁷ | 0 | At equilibrium |
Formula note
E = E° − (RT / nF) × ln(Q) — full Nernst equation
E = E° − (0.05916 / n) × log₁₀(Q) — at 25 °C only
ΔG = −nFE ΔG° = −nFE° ln(K) = nFE° / RT
Constants used: R = 8.314 J mol⁻¹ K⁻¹ · F = 96 485 C mol⁻¹ · T(K) = T(°C) + 273.15.
All calculations run entirely in your browser — no data is sent to any server.