Electrochemical Cell EMF & Nernst Calculator

Electrochemistry, Cell Thermodynamics & Nernst Equation Metrology

Electrochemical cell potential quantifies the maximum electrical work available from a redox reaction:

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• Standard Cell Potential Formula (IUPAC Standards)**:

E^_cell = E^_cathode (reduction) - E^_anode (oxidation)

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• The Nernst Equation (Non-Standard Conditions)**:

E_cell = E^_cell - (RT) / (nF) Q = E^_cell - (2.302585 RT) / (nF)_10 Q

At 298.15 K (25^): E_cell = E^_cell - (0.05916) / (n)_10 Q

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• Gibbs Free Energy & Equilibrium Constant**:

Δ G = -n F E_cell

Δ G^ = -n F E^_cell = -RT K _10 K = n F E^_cell2.302585 RT

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• Standard Electrochemical Cell Benchmarks (298.15 K)**:

• Daniell Cell: E^_cell = 1.100 V Δ G^ = -212.3 kJ/mol

• Daniell Cell: E_cell = 1.159 V Δ G = -223.7 kJ/mol

• Lead-Acid Battery Cell: E^_cell = 2.050 V Δ G^ = -395.6 kJ/mol

• H₂/O₂ Fuel Cell: E^_cell = 1.230 V Δ G^ = -474.7 kJ/mol

How to Use This Calculator

Enter your Cathode Standard Reduction Potential (E° cathode) (e.g. 0.34 in V), Anode Standard Reduction Potential (E° anode) (e.g. -0.76 in V), Number of Electrons Transferred (n) — choose from n = 1 electron (e.g. Ag⁺/Ag, Li⁺/Li, Fe³⁺/Fe²⁺), n = 2 electrons (e.g. Cu²⁺/Cu, Zn²⁺/Zn, Pb²⁺/Pb), n = 3 electrons (e.g. Al³⁺/Al, Fe³⁺/Fe), Reaction Quotient (Q = [Products]/[Reactants]) (e.g. 0.01 in Q), Temperature (Kelvin - K) (e.g. 298.15 in K), and Electrochemical Cell Benchmark — choose from Custom Galvanic / Electrolytic Cell, Daniell Cell (Cu²⁺/Cu +0.34V vs Zn²⁺/Zn -0.76V, Q=0.01) → E°=1.100V | E_cell=1.159V (ΔG = -223.7 kJ/mol), Daniell Cell Standard (Q=1.000, 1.0M ions) → E_cell = 1.100V (ΔG° = -212.3 kJ/mol). Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Standard Cell Potential: E°_cell = E°_cathode - E°_anode

Nernst Equation: E_cell = E°_cell - (RT / nF) * ln(Q)

Gibbs Free Energy: deltaG = -n F E_cell (in J/mol -> converted to kJ/mol)

Equilibrium Constant log10(K) = (n F E°_cell) / (2.302585 R T)

Worked Example

A chemistry student analyzing a classic copper-zinc Daniell cell finds that when zinc product ions are diluted relative to copper reactant ions, the Nernst equation boosts the cell voltage from 1.100 V to 1.159 V, driving a spontaneous Δ G of -223.7 kJ/mol.

Understanding Your Result

Scientific calculations require careful attention to significant figures and units. Your result is only as precise as your least precise input — expressing the result with more significant figures than the inputs implies false precision. For laboratory or regulatory work, verify which measurement standard applies (SI, ASTM, ISO) and whether temperature, pressure, or concentration conditions affect the formula. Cross-reference results against published reference values for your specific material or compound.