Electrochemical Cell Potential Calculator

Calculate standard cell potential E°cell from half-reaction reduction potentials.

Cathode reduction potential E°red (V) (V)

Cu²⁺/Cu: +0.34, Ag⁺/Ag: +0.80

Anode reduction potential E°red (V) (V)

Zn²⁺/Zn: -0.76, Fe²⁺/Fe: -0.44

Number of electrons transferred n

Temperature T (K) (K)

Reaction quotient Q (for Nernst)

1 = standard conditions

Please check your inputs and try again.

How Cell Potential Works

Every redox reaction can be split into two half-reactions. Standard reduction potentials rank how strongly each species pulls electrons, and the difference between the two determines whether the reaction runs spontaneously.

E°_cell = E°_cathode − E°_anode

Both values in that expression are reduction potentials as tabulated. You do not reverse the sign of the anode value before subtracting — the subtraction already accounts for the anode running in reverse. This is the single most common error in the calculation.

Sign of E°_cell	ΔG°	Cell type	Behaviour
Positive	Negative	Galvanic	Runs spontaneously, produces electricity
Negative	Positive	Electrolytic	Requires applied voltage to proceed
Zero	Zero	At equilibrium	No net current flows

ΔG° = −nFE°_cell

The link to free energy is direct: n is the number of electrons transferred and F is the Faraday constant, 96,485 C/mol. A positive cell potential therefore always corresponds to a negative ΔG° — the two statements are the same physics in different units.

Away from Standard Conditions

E_cell = E°_cell − (RT/nF) ln Q

Standard potentials assume 1 M concentrations, 1 atm partial pressures and 298 K. Real cells rarely meet those conditions, and the Nernst equation corrects for it. At 298 K the prefactor simplifies to 0.0592/n when using log₁₀, which is the form usually memorised.

As a cell discharges, products accumulate, Q rises, and E_cell falls — which is exactly why a battery’s voltage sags as it is used. When Q reaches K, E_cell hits zero and the battery is flat.

Worked Examples

Example 1: Zn-Cu cell: Ecat=+0.34V, Ean=-0.76V, n=2

Ecell=0.34-(-0.76)

Result: E°=1.10V — classic Daniell cell

Spontaneous galvanic cell

Example 2: Electrolysis of water: Ecat=-0.83V, Ean=+1.23V

Ecell=-0.83-1.23=-2.06V

Result: Non-spontaneous, need >2.06V applied

Water splitting requires external power

Example 3: Concentration effect

Daniell cell, E° = 1.10 V, but [Zn²⁺] = 1.0 M and [Cu²⁺] = 0.001 M

Result: E = 1.10 − (0.0592/2)log(1000) = 1.01 V

Q = [Zn²⁺]/[Cu²⁺] = 1000. Lowering the cathode reactant concentration reduces the driving force by about 89 mV.

Example 4: Free energy from potential

E° = 1.10 V, n = 2 electrons

Result: ΔG° = −2 × 96,485 × 1.10 = −212 kJ/mol

Strongly negative, confirming spontaneity. This conversion links electrochemistry directly to thermodynamic tables.

Example 5: Balancing does not scale potential

Half-reaction doubled to balance electrons

Result: E° unchanged, ΔG° doubled

Potential is energy per coulomb, an intensive property. Free energy is total energy, an extensive one — which is why only ΔG scales.

Common Mistakes

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Reversing the anode sign before subtracting

Use tabulated reduction potentials for both electrodes and subtract. Flipping the anode sign first double-counts the reversal and gives an answer wrong by twice the anode potential.

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Multiplying potentials when balancing electrons

Cell potential is intensive — it does not scale with the amount of substance. Doubling a half-reaction to balance electrons does not double its potential, even though it does double ΔG.

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Assuming a positive E° means a fast reaction

Cell potential is thermodynamic. Many spontaneous electrochemical reactions are kinetically slow and need catalysts or elevated overpotential to proceed usefully.

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Ignoring the difference between E° and E

Standard potential applies at 1 M and 298 K. Real concentrations shift the actual potential through the Nernst equation, sometimes enough to reverse which direction is spontaneous.

Frequently Asked Questions

Galvanic vs electrolytic cell?

Galvanic: E°>0, spontaneous, converts chemical to electrical energy (batteries). Electrolytic: E°<0, non-spontaneous, uses electrical energy for chemistry (electroplating, electrolysis). Same electrochemistry principles.

Standard conditions?

E° measured at 25°C, 1M concentrations, 1 atm gas pressure. For non-standard: use Nernst equation. Q=1 at standard conditions → E=E°.

How do I calculate standard cell potential?

Subtract the anode’s standard reduction potential from the cathode’s. Use tabulated reduction values for both — do not reverse the anode sign beforehand.

What does a negative cell potential mean?

The reaction is not spontaneous as written. It corresponds to an electrolytic cell, which requires an applied voltage exceeding the magnitude of E° to proceed.

Why doesn’t potential scale when balancing electrons?

Potential is energy per unit charge, an intensive property like temperature. Doubling the reaction doubles both the charge and the energy, so the ratio is unchanged.

When do I need the Nernst equation?

Whenever concentrations differ from 1 M or temperature from 298 K. It explains why battery voltage falls during discharge as reactants deplete and products accumulate.

What is the relationship between E° and ΔG°?

ΔG° = −nFE°. A positive cell potential always corresponds to a negative free energy change, since both describe the same spontaneity in different units.

Formula Explorer connections

Interpretation: This formula links electron transfer, charge, potential, current or ionic transport in an electrochemical system. Assumption: Balance electron count and half-reactions, preserve sign conventions, and use consistent concentration, temperature and electrical units. Real cells include losses and overpotential.

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