Electrochemical Cell Potential Calculator

An electrochemical cell generates voltage by coupling two half-reactions: an oxidation at the anode and a reduction at the cathode. The total cell potential is the difference between their standard reduction potentials.

E°cell = E°cathode - E°anode

Standard reduction potentials are measured relative to the standard hydrogen electrode (SHE), defined as 0.000 V. A positive E°cell means the reaction is spontaneous under standard conditions (1 M concentrations, 1 atm, 25°C).

Some common standard reduction potentials (E° vs SHE):

• Zn²⁺ + 2e⁻ → Zn: -0.76 V (commonly the anode in zinc-based cells)
• Fe²⁺ + 2e⁻ → Fe: -0.44 V
• 2H⁺ + 2e⁻ → H₂: 0.00 V (reference electrode)
• Cu²⁺ + 2e⁻ → Cu: +0.34 V
• Ag⁺ + e⁻ → Ag: +0.80 V
• Cl₂ + 2e⁻ → 2Cl⁻: +1.36 V

A classic zinc-copper Daniell cell: E°cell = 0.34 - (-0.76) = 1.10 V

The relationship to Gibbs free energy:

ΔG° = -n × F × E°cell

Where n = moles of electrons transferred and F = Faraday’s constant (96,485 C/mol). A negative ΔG° confirms the reaction is thermodynamically favorable.

The equilibrium constant Keq can also be found: log(Keq) = n × E°cell / 0.05916 (at 25°C).

Note: the Nernst equation adjusts E°cell for non-standard concentrations. E = E° - (RT/nF) × ln(Q), which at 25°C simplifies to E = E° - (0.05916/n) × log(Q).

Note which logarithm goes with which constant. The RT/nF form takes a natural log; the 0.05916 shortcut has the conversion to base 10 already folded into the constant, so it takes log₁₀. Mixing them up scales your correction by a factor of 2.303, which is more than enough to turn a plausible answer into a wrong one.

What the standard in “standard potential” is doing

Every value in the table is measured against the same reference, the standard hydrogen electrode, which is defined as exactly 0 V. Nothing about hydrogen makes it a natural zero. You cannot measure a single electrode in isolation at all, only the difference between two, so the scale needs an arbitrary origin and hydrogen was the one chosen. This is why the numbers can be negative without anything being physically odd: a negative potential just means the couple is a poorer oxidising agent than hydrogen.

“Standard” also carries real conditions: 1 M concentrations for solutes, 1 bar for gases, 25 °C, and pure solids. Depart from those and you need the Nernst equation above. In practice concentration effects are modest, around 59 mV per decade for a one-electron couple, which is exactly why a fresh battery and a half-flat one read almost the same voltage right up until they do not.

Spontaneous is not the same as fast

A positive E°cell says the reaction can happen and will release energy. It says nothing about how long you will wait. Hydrogen and oxygen sit together indefinitely at room temperature despite an enormously favourable cell potential, until a spark or a catalyst gives them a route.