Faraday Electrolysis Calculator
Metal plated from current, time, molar mass, and electron count.
What it does
Electroplating turns electricity into metal weight. Run current through a cell for a set time and ions land on the cathode in strict proportion to the electrons delivered. Jewelers, PCB shops, and refineries all cost jobs on this proportion.
The tool above applies Faraday law directly. Enter amps, hours, the metal molar mass, and electrons per ion to get deposited grams, total coulombs, and moles of electrons. The copper default (2 A, 1 hour, 63.55 g/mol, 2 electrons) plates 2.37 g from 7,200 C.
Both halves of the math are university standard. Chemistry LibreTexts electrolysis pages define charge as current times time and convert with the 96,485 C/mol Faraday constant, and NIST electrochemical papers formalize the same constant from silver equivalent weight work. The example on this page mirrors their textbook silver problem at a smaller scale.
Theory assumes every electron builds metal. Side reactions, heat, poor contacts, and wrong bath chemistry all steal current, so shops derate by measured efficiency, often 90 to 98 % for copper and far less for chromium. Plan metal from theory, then order extra for the inefficiency.
How to use
- Type the cell current in amps.
- Type the plating time in hours.
- Type the metal molar mass in g/mol.
- Type electrons per ion for that metal.
- Read deposited mass first, then charge and moles.
- Divide mass by your cell efficiency for ordering.
Formula
- Q
- Charge in coulombs (amps x seconds).
- I
- Current in amps.
- t
- Time in seconds (hours x 3600).
- n
- Moles of electrons delivered.
- M / z
- Molar mass over electrons per ion.
One mole of electrons (a Faraday, 96,485 C) plates one mole of silver (z = 1) but only half a mole of copper (z = 2) or a third of aluminum (z = 3). Time must reach the formula in seconds, hence the 3600 fold from hours. Current efficiency below 100 % scales the mass down proportionally.
Worked example
Example: copper at 2 A for 1 hour
Defaults already filled in the form.
- Seconds: 1 x 3600 = 3600 s.
- Charge: 2 x 3600 = 7,200 C.
- Moles of electrons: 7,200 / 96,485 = 0.075 mol e-.
- Copper moles: 0.075 / 2 = 0.0373 mol Cu.
- Mass: 0.0373 x 63.55 = 2.37 g.
- Tool shows 2.37 g from 7,200 C and 0.075 mol e-.
Reference table
| Metal | Molar mass, z | Plated |
|---|---|---|
| Silver Ag+ | 107.9, z = 1 | 8.05 g |
| Copper Cu2+ | 63.55, z = 2 | 2.37 g |
| Nickel Ni2+ | 58.69, z = 2 | 2.19 g |
| Aluminum Al3+ | 26.98, z = 3 | 0.67 g |
Limits
- 100 % current efficiency assumed; real cells run lower.
- Pure single metal assumed; alloys split current by chemistry.
- Steady current assumed; pulsing and ramping need integration.
- Says nothing about adhesion, brightness, or coverage quality.
Common mistakes
- Entering minutes as hours, inflating charge 60 fold.
- Using atomic number instead of electrons per ion.
- Forgetting the divide by z for copper, nickel, and aluminum.
- Ordering exact theory mass with no efficiency margin.
- Confusing cathode deposit with anode loss in impure baths.
Try it yourself
Quick checks. Answers sit tucked under each question.
Aluminum at 5 A for 2 hours. Theory mass?
36,000 C gives 0.373 mol e-, mass 0.373 x 26.98 / 3 = 3.36 g.
Silver at 2 A for 1 hour. Mass?
0.075 mol e- x 107.9 / 1 = 8.05 g. Monovalent ions plate fastest per coulomb.
Copper cell runs at 90 % efficiency. Expected from the example?
2.37 x 0.9 = 2.13 g.
Questions
What is the Faraday constant?
96,485 coulombs per mole of electrons, the charge of one mole of electrons.
Why divide by electrons per ion?
Each deposited atom consumes z electrons, so z moles of electrons yield one mole of metal.
Does voltage matter here?
Not for mass. Voltage must exceed the reaction threshold, but coulombs count the metal.
Why did my cell plate less?
Side reactions and resistance waste current; measure efficiency and derate.
Can this strip mass too?
Yes. Anode loss follows the same math in ideal baths.
What is a coulomb?
One amp for one second.
Sources
- Chemistry LibreTexts: Electrolysis quantitative aspects
- NIST: electrochemical equivalent and the Faraday (J Res paper)