Faraday’s law of electrolysis
Faraday’s law relates electrical charge to the amount of chemical transformation at an electrode. Charge equals current multiplied by time, and one mole of electron charge is represented by the Faraday constant.
The calculated mass is theoretical at 100% current efficiency with one specified electrode reaction. Side reactions, changing valence, mass-transfer limits, dissolution, impurities, and incomplete recovery reduce or alter measured yield.
How to use the Faraday electrolysis calculator
- Choose the unknown: Select mass, molar mass, current, time, or electron transfer number.
- Enter reaction data: Use the correct product molar mass and balanced half-reaction electron count.
- Calculate theoretical yield: Review the ideal 100%-current-efficiency result.
- Apply process efficiency: Use measured current efficiency and recovery separately for real electrolysis or plating.
Formula and variables
Current I for time t supplies charge It. Dividing by nF gives reacted moles, then multiplying by molar mass M gives theoretical mass.
m = MIt/(nF)- m — Deposited mass
- Theoretical electrode product mass (g)
- M — Molar mass
- Molar mass of deposited or reacted species (g/mol)
- I — Current
- Electric current (A)
- t — Time
- Electrolysis duration (s)
- n — Electron number
- Stoichiometric moles of electrons per mole of product
- F — Faraday constant
- Molar charge constant (C/mol)
Copper deposition example
Pass 10 A for 3,600 s to reduce Cu²⁺ using M = 63.546 g/mol and n = 2.
- Current and time
- 10 A for 3,600 s
- Copper molar mass
- 63.546 g/mol
- Electrons
- 2 mol e⁻/mol Cu
- m = 63.546 × 10 × 3,600/(2 × 96,485.33212)
- m ≈ 11.85 g
Result: The theoretical copper mass is approximately 11.85 g.
Actual deposited and recovered mass will differ when current efficiency is below 100% or material is lost.
Understanding your results
Distinguish theoretical and actual yield
The formula converts charge stoichiometrically under an ideal single reaction.
- One ampere equals one coulomb per second.
- Electron count comes from the balanced half-reaction.
- Current efficiency accounts for charge consumed by competing processes.
- Mass recovery can differ from electrochemical production.
Assumptions
- Current is constant or the entered value is its correct time average.
- The half-reaction and electron stoichiometry are correct.
- Current efficiency and product recovery are 100%.
Limitations
- Does not model current efficiency, side reactions, concentration polarization, overpotential, changing current, electrode area, mass transfer, dissolution, or recovery losses.
- Does not balance electrochemical reactions.
- The Faraday constant value follows the implemented constant and should be reported with appropriate precision.
Common mistakes
- Entering hours instead of seconds.
- Using charge number without balancing the actual half-reaction.
- Treating theoretical mass as guaranteed plating yield.
- Mixing grams and kilograms for molar mass or result.
Practical use cases
Electroplating estimates
Estimate theoretical deposited mass for a known current and duration.
Electrochemistry education
Connect charge, electron moles, reaction stoichiometry, and product mass.
Frequently asked questions
Why is actual mass lower than calculated?
Side reactions, less than 100% current efficiency, dissolution, incomplete recovery, and measurement effects can lower yield.
How do I choose n?
Use the number of electrons per mole of product in the balanced electrode half-reaction.
Can current vary with time?
Use integrated charge or a valid time-average current; a simple instantaneous value may be inaccurate.
Sources and review
- Fundamental Physical Constants — National Institute of Standards and Technology. Accessed 2026-07-13.
Reviewed 2026-07-13.