Electrolysis calculator (Faraday’s laws)
Pick the metal or gas — copper, silver, zinc, nickel, hydrogen, oxygen and others are preset — or enter any molar mass and charge number. Then enter the current and time to get the mass, or the mass you want to get the time or current. A current efficiency below 100 % accounts for side reactions.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: the mass, the time or the current.
- Pick the substance, or “Other” to type a molar mass and the number of electrons z.
- Enter the two known quantities: current in amperes, time in s, min or h, or the mass in grams.
- Lower the current efficiency if side reactions use part of the current.
m = I × t × η × M ÷ (z × F)
- I current (A), t time (s), η current efficiency, M molar mass (g/mol), z electrons per formula unit
- F = 96,485.33212 C/mol, the charge of one mole of electrons
- Time: t = m × z × F ÷ (M × η × I); current: I = m × z × F ÷ (M × η × t)
Molar masses come from the standard atomic weights in the periodic table (Cu 63.546, Ag 107.87, Ni 58.693 g/mol). Gas volumes use 22.414 L/mol at 0 °C and 1 atm.
Worked example
Copper plating at 2 A for 1 hour: Q = 2 × 3600 = 7,200 C, that is 7200 ÷ 96,485.33212 = 0.074623 mol of electrons. Each Cu²⁺ takes two, so 0.037311 mol of copper = 0.037311 × 63.546 = 2.371 g.
Plating 5 g of nickel at 3 A: Q = 5 × 2 × 96,485.33212 ÷ 58.693 = 16,438.98 C, so t = 16,438.98 ÷ 3 = 5,480 s = 1.5221 h (91.33 min).
Tips
- Seconds in the formula. 1 h is 3600 s; the calculator converts minutes and hours for you.
- Charge in A·h. Battery capacity in ampere-hours is charge too: 1 A·h = 3600 C.
- Plating thickness. Divide the mass by the metal’s density and the plated area to estimate the layer thickness.
Frequently asked questions
What are Faraday’s laws of electrolysis?
The first law: the mass changed at an electrode is proportional to the charge passed. The second: for the same charge, masses are proportional to M ÷ z. Together, m = Q × M ÷ (z × F), with Q = I × t and the Faraday constant F = 96,485.33212 C/mol.
What is z?
The number of electrons needed per formula unit: 2 for Cu²⁺ + 2e⁻ → Cu, 1 for silver, 3 for aluminium, 4 for oxygen (2H₂O → O₂ + 4H⁺ + 4e⁻). Use the charge of the ion in your bath; nickel or copper from other salts may need a different z.
What is current efficiency?
The share of the current that actually drives the wanted reaction. In plating some current also produces hydrogen; at 90 % efficiency only 90 % of the charge deposits metal, so the mass is 10 % lower or the time 11 % longer.
How much hydrogen does electrolysis of water make?
Each mole of H₂ needs 2 moles of electrons, 192,971 C. One ampere for one hour (3600 C) gives 0.01866 mol, about 0.418 L at 0 °C and 1 atm. Oxygen needs twice as many electrons per molecule, so half that volume forms at the anode.