About the Electrolysis Calculator (Faraday's Law)
This electrolysis calculator applies Faraday's laws of electrolysis to connect electric charge with the amount of substance produced at an electrode. Pick a metal or gas (or enter your own molar mass and electrons transferred), then solve for the mass deposited, the plating time needed, or the current required.
It is useful for chemistry students working electrochemistry problems, hobbyists electroplating copper or nickel, and anyone estimating how long an electrolysis run will take. Charge, moles of electrons and moles of product are shown alongside the answer so you can follow every step.
Real cells rarely convert every coulomb into product — side reactions such as hydrogen evolution waste some current. Use the current-efficiency field to account for this; 100% gives the theoretical Faraday result. The Faraday constant used is the exact SI value, 96,485.33212 C/mol.
With the default inputs, the answer is 1.1855. Change any value above to recalculate instantly.
How to use the electrolysis calculator (faraday's law)
- 1Choose what to solve for: mass, time or current.
- 2Pick the metal or gas, or choose Custom and enter its molar mass and electrons transferred.
- 3Enter the known current, time and/or target mass.
- 4Set the current efficiency (100% for textbook problems).
- 5Read the answer, then check the charge and moles of electrons for your working.
Formula and method
Faraday's first law says the mass of substance produced at an electrode is proportional to the charge passed, Q = I × t. Dividing the charge by the Faraday constant F (96,485.33212 C per mole of electrons) gives moles of electrons; dividing by n, the electrons needed per atom or molecule, gives moles of product; multiplying by the molar mass M gives grams.
Faraday's second law follows from the same equation: for the same charge, the masses of different substances are proportional to M/n, their equivalent weights. The current efficiency η scales the useful charge to allow for side reactions. Rearranging the single equation lets the calculator solve for time or current instead of mass.
- m
- Mass of substance produced (g)
- I
- Current (A)
- t
- Time (s)
- M
- Molar mass (g/mol)
- n
- Electrons transferred per formula unit
- F
- Faraday constant, 96,485.33212 C/mol
- η
- Current efficiency (fraction)
Worked examples
Copper plated at 2 A for 30 minutes
Charge = 2 A × 1,800 s = 3,600 C, which is 3,600 ÷ 96,485 = 0.03731 mol of electrons. Copper needs 2 electrons per atom, so 0.018656 mol Cu × 63.546 g/mol ≈ 1.185 g.
Time to plate 1.5 g of silver at 0.5 A
1.5 g Ag ÷ 107.868 g/mol = 0.013906 mol, and silver needs one electron per atom, so Q = 0.013906 × 96,485 = 1,341.7 C. At 0.5 A that takes 2,683 s, about 44.7 minutes.
Current to deposit 0.25 g of gold in 2 hours at 90% efficiency
Gold(III) needs 3 electrons per atom: Q = 0.25 ÷ 196.967 × 3 × 96,485 = 367.4 C of useful charge. Spread over 7,200 s at 90% efficiency, I = 367.4 ÷ (7,200 × 0.9) ≈ 0.0567 A.
Frequently asked questions
What are Faraday's laws of electrolysis?+
The first law says the mass of substance formed at an electrode is proportional to the electric charge passed. The second law says that, for the same charge, the masses of different substances are proportional to their molar mass divided by the electrons transferred (their equivalent weight).
What is the Faraday constant?+
The Faraday constant F is the charge carried by one mole of electrons: 96,485.33212 C/mol. Since the 2019 SI redefinition it is exact, because it equals the elementary charge times the Avogadro constant.
How do I find n, the number of electrons?+
Use the half-reaction at the electrode. Cu²⁺ + 2e⁻ → Cu gives n = 2; Ag⁺ + e⁻ → Ag gives n = 1; 2H₂O → O₂ + 4H⁺ + 4e⁻ gives n = 4 per O₂ molecule.
Why is my real plating mass lower than calculated?+
Some current is consumed by side reactions, most often hydrogen gas evolution at the cathode, and some deposit may be lost or poorly adherent. Enter a current efficiency below 100% to model this, ideally a value measured by weighing a test deposit from your own bath.
How do I convert ampere-hours to coulombs?+
One ampere-hour is 3,600 coulombs (1 A for 3,600 s). One mole of electrons, 96,485 C, is therefore about 26.8 A·h.