Redox Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: August 19, 2026Electricity from a Difference in Willingness to Grab Electrons
Every element has a measured tendency to either gain or give up electrons, expressed as a standard reduction potential. Pair two half-reactions with different potentials and electrons flow spontaneously from one to the other — that flow is the current in a battery. The size of the voltage is just the gap between the two potentials.
The Formula
Both values are standard reduction potentials, in volts, referenced to the standard hydrogen electrode. A positive E(cell) means the reaction is spontaneous as written (galvanic); a negative value means it needs an external power source to run (electrolytic).
Where This Calculation Matters
- Battery design — choosing electrode materials with a large potential gap maximizes cell voltage.
- Corrosion prediction — two dissimilar metals in contact form a galvanic cell, and the potential difference predicts which one corrodes.
- Electroplating — plating processes rely on driving a normally non-spontaneous reduction using an external voltage.
- Analytical electrochemistry — predicting whether a redox titration or sensor reaction will proceed as intended.
Standard Cell Voltages from Published Reduction Potentials
| Cathode (reduction) | Anode (reduction potential shown) | E(cell) |
|---|---|---|
| Cu2+/Cu (+0.34 V) | Zn2+/Zn (−0.76 V) | 1.10 V |
| Ag+/Ag (+0.80 V) | Cu2+/Cu (+0.34 V) | 0.46 V |
| Cu2+/Cu (+0.34 V) | Fe2+/Fe (−0.44 V) | 0.78 V |
The first row is the classic zinc-copper (Daniell) cell, historically one of the earliest practical batteries, with a well-documented standard voltage of 1.10 V.
How to Use This Calculator
- Enter the Standard Reduction Potential – Cathode (V) for the half-reaction being reduced.
- Enter the Standard Reduction Potential – Anode (V) for the half-reaction being oxidized.
- Select Calculate to get the overall cell potential and whether the reaction is spontaneous.
Related Calculations
Once a redox reaction's stoichiometry is set, the Chemical Equation Balancer can confirm the overall equation balances. For converting between moles of electrons and mass transferred, see the Moles Calculator.
Electrochemical Fundamentals of Reduction-Oxidation Systems
Redox (reduction-oxidation) processes encompass chemical reactions characterized by the fundamental transfer of electrons between participating atomic, ionic, or molecular species. In every redox couple, oxidation represents the algebraic loss of electrons accompanied by an increase in oxidation state (OIL: Oxidation Is Loss), while reduction represents the gain of electrons accompanied by a decrease in oxidation state (RIG: Reduction Is Gain).
In this galvanic couple, metallic zinc undergoes two-electron oxidation (reducing agent), while cupric ions undergo two-electron reduction (oxidizing agent).
Standard Reduction Potentials and Cell Voltage
The driving thermodynamic force of an electrochemical cell is its standard electromotive force (E°cell), measured in Volts (1 V = 1 Joule/Coulomb). Relative electron affinity is tabulated against the Standard Hydrogen Electrode (SHE, defined as E° = 0.000 V at 25°C, 1 atm H2, and 1.0 M H+):
A positive standard cell potential (E°cell > 0) indicates a thermodynamically spontaneous reaction under standard conditions (298.15 K, 1.0 M solute concentrations, 1.0 bar gas partial pressures).
The Nernst Equation for Non-Standard Concentrations
Under operating conditions where reactant and product concentrations diverge from 1.0 M unity, the actual cell potential is governed by the Nernst Equation:
Where R is the universal gas constant (8.314 J/mol·K), T is absolute temperature (K), z is the number of moles of electrons transferred per reaction cycle, F is the Faraday constant (96,485.3 Coulombs/mol e-), and Q is the reaction quotient. At 25°C (298.15 K), the equation simplifies using base-10 logarithms to: Ecell = E°cell - (0.05916 / z) × log10(Q).
Gibbs Free Energy and Equilibrium Relations
Electrochemistry directly bridges chemical equilibrium with thermodynamic work:
- Free Energy Relation: ΔG° = -z × F × E°cell. A positive voltage yields negative free energy (ΔG° < 0), confirming exergonic spontaneity.
- Equilibrium Constant (K): ln(K) = (z × F × E°cell) / (R × T), demonstrating that cell voltage directly determines chemical equilibrium constants.
Step-by-Step Worked Calculation Example
Example: Calculating Voltage of a Non-Standard Daniell Galvanic Cell
Problem: A Daniell galvanic cell operates at 298.15 K with a zinc anode in 0.010 M ZnSO4 and a copper cathode in 2.00 M CuSO4. Standard reduction potentials are: E°(Cu2+/Cu) = +0.340 V and E°(Zn2+/Zn) = -0.763 V. Determine: (1) The standard cell potential E°cell; (2) The reaction quotient Q; and (3) The actual operational cell voltage Ecell.
Step 1: Compute standard cell voltage:
E°cell = E°cathode - E°anode = +0.340 V - (-0.763 V) = +1.103 Volts
Step 2: Determine reaction quotient Q (z = 2 electrons transferred):
Overall reaction: Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)
Q = [Zn2+] / [Cu2+] = 0.010 M / 2.00 M = 0.0050
Step 3: Apply the Nernst equation:
Ecell = 1.103 V - (0.05916 / 2) × log10(0.0050)
Ecell = 1.103 V - (0.02958) × (-2.3010) = 1.103 V + 0.0681 V = 1.171 Volts
Conclusion: The non-standard Daniell cell generates an operating potential of 1.171 Volts.
Industrial and Technological Applications
- Lithium-Ion Battery Storage: Intercalation redox couples between lithium cobalt oxide cathodes and graphite anodes govern charge and discharge cycles in modern electric vehicles.
- Cathodic Protection against Corrosion: Sacrificial magnesium or zinc anodes oxidize preferentially to protect subterranean steel natural gas pipelines and marine ship hulls.
- Electrolytic Metal Refining: Industrial electrowinning purifies raw copper blister to 99.99% cathode purity in copper refineries worldwide.
Pourbaix Diagrams and Metal Passivation in Corrosion Engineering
In materials science and metallurgical engineering, Pourbaix diagrams (potential-pH diagrams) map thermodynamic stability regions for metals in aqueous environments. By plotting electrochemical electrode potential (ESHE) against pH, materials engineers determine whether a structural alloy (such as 316L stainless steel, titanium, or structural mild steel) will undergo active uniform corrosion, form an insoluble protective passivation oxide film (such as Cr2O3 or TiO2), or remain completely immune to oxidation in marine and chemical plant environments.
Fuel Cell Electrochemistry and Polymer Electrolyte Membranes
Proton-exchange membrane fuel cells (PEMFC) generate clean electrical power by splitting gaseous hydrogen at a platinum catalyst anode (H2 → 2H+ + 2e-, E° = 0.000 V) and reducing atmospheric oxygen at the cathode (O2 + 4H+ + 4e- → 2H2O, E° = +1.229 V). Electrochemical engineers calculate cell overpotentials (activation, ohmic, and mass-transport losses) to maximize operating efficiency and current density in hydrogen electric heavy transport vehicles.
Electrochemical Sensor Potentiometry and Biosensors
In modern clinical diagnostics and continuous glucose monitors (CGMs), immobilized glucose oxidase enzymes catalyze glucose oxidation, generating hydrogen peroxide that undergoes electrochemical oxidation on platinum microelectrodes to output nanoampere currents proportional to blood sugar concentration.