Standard Cell Potential Calculator – From Half-Reactions to Volts, ΔG° and K
A galvanic cell pairs two half-reactions: reduction at the cathode and oxidation at the anode. This calculator takes any two couples from a table of 54 standard reduction potentials, or your own values. It works out which electrode is which, balances the electrons and writes the overall equation and cell notation. It then gives E°cell, ΔG°, the equilibrium constant K and, at real concentrations, the Nernst equation voltage.
Why every potential needs a reference
You can only measure a voltage between two electrodes. Chemists therefore define the standard hydrogen electrode (SHE), H⁺(aq, 1 M) | H₂(g, 1 bar) | Pt, as exactly 0 V and quote every other couple against it. Labs often use a calomel (SCE, +0.241 V) or Ag/AgCl (+0.197 V) reference instead. Switching the reference moves both electrodes by the same amount, so E°cell never changes. The "Potentials shown vs" setting lets you check this.
Reading the electrochemical series
In the series, strong oxidizing agents (F₂, MnO₄⁻) sit at the top and strong reducing agents (Li, K) at the bottom. In a galvanic cell the higher couple is the cathode. The ladder chart shows the gap between the two couples, which is the cell voltage, and the band of potentials in which water itself is stable.
The Daniell cell, step by step
For copper and zinc, E°cell = E°cathode − E°anode = 0.3419 − (−0.7618) = +1.1037 V. Both values are reduction potentials. The usual mistake is to flip the sign of the anode's potential and subtract it, which counts the reversal twice. The cell notation is Zn(s) | Zn²⁺(aq) ‖ Cu²⁺(aq) | Cu(s), with the anode on the left. To check oxidation states in a less familiar couple, use the Oxidation Number Calculator.
Why E° is never multiplied
A volt is a joule per coulomb, so E° is intensive. When Ag⁺ + e⁻ → Ag is doubled to match copper's two electrons, its E° stays +0.7996 V. What doubles is ΔG° = −nFE°, through n.
E°, ΔG° and K
Because log₁₀K = nE°/(0.05916 V) at 25 °C, a small voltage means a huge K. The Daniell cell's K is about 2 × 10³⁷, so the reaction goes to completion, and each millivolt of E° moves K by about 8 % when n = 2. The second tab converts directly between E°, ΔG° and K. For K from measured equilibrium amounts, use the Equilibrium Constant Calculator.
The Nernst equation in practice
Concentration enters only through a logarithm, so a battery's voltage barely sags until a reactant runs out. A concentration cell, the same couple at two concentrations, runs on the logarithm alone. pH can still flip the answer: Q for permanganate oxidizing chloride contains [H⁺]¹⁶. The reaction is spontaneous at pH 0, but by pH 3 E has fallen to −0.135 V.
Temperature coefficients and thermodynamics
The slope of E° against temperature gives the entropy change, ΔS° = nF·(dE°/dT), and ΔH° then follows. For the hydrogen fuel cell, ΔG°/ΔH° caps the efficiency at about 83 %. The table's coefficients are derived from standard entropies, like those in the Entropy Change Calculator.
Combining half-reactions
Potentials of consecutive steps don't add, but their ΔG° values do. The third tab weights each E° by its electrons, draws Latimer and Frost diagrams, and flags species that disproportionate, such as Cu⁺ and H₂O₂.
The formulas
E°cell = E°(cathode) − E°(anode)
ΔG° = −n·F·E°
log₁₀K = n·F·E° / (R·T·ln 10)
E = E° − (R·T / n·F)·ln Q
E°(combined) = Σ eᵢ·E°ᵢ / Σ eᵢ