Electrolysis & Electroplating Calculator (Faraday)

Understanding the electrolysis and electroplating calculator — concept and principle

Faraday's laws of electrolysis connect electric charge with the amount of substance produced at an electrode. This calculator estimates how many grams of metal a current deposits in a given time and, from the metal's density and the plated area, the average coating thickness. Platers, students and hobbyists use it to plan plating times, size power supplies and check lab results.

Charge counts electrons; two electrons plate one Cu atom, giving 1.126 g and a 25.1 µm coat here.

How it is calculated

m = (I × t × M) / (n × F) × (efficiency / 100)

thickness (µm) = m / (ρ × A) × 10⁴

I is the current in amperes, t the time (entered in minutes and multiplied by 60 to give seconds), M the molar mass in g/mol, n the number of electrons needed per ion (2 for Cu²⁺, 1 for Ag⁺, 3 for Cr³⁺), and F = 96485.33212 C/mol, the Faraday constant. Current efficiency is the share of charge that actually deposits metal. Dividing the mass by density ρ (g/cm³) gives the volume in cm³; dividing by area A (cm²) gives thickness in cm, and × 10⁴ converts it to micrometres.

The principle

Charge is carried by electrons, and each metal ion needs a fixed number of them to become an atom. One mole of electrons carries F coulombs, so the charge I × t corresponds to I·t/F moles of electrons and I·t/(nF) moles of metal. Multiplying by M gives grams. This is Faraday's first law (mass proportional to charge) and second law (mass proportional to M/n for the same charge). Efficiency below 100% accounts for side reactions such as hydrogen evolution.

Worked example

Default: copper (M = 63.546 g/mol, Cu²⁺ + 2e⁻ → Cu).

Inputs: I = 2 A, t = 30 min, n = 2, efficiency 95%, ρ = 8.96 g/cm³, A = 50 cm².
Charge: 2 × 30 × 60 = 3600 C, which is 3600 ÷ 96485.33 = 0.037311 mol of electrons.
Copper: 0.037311 ÷ 2 = 0.018656 mol; × 63.546 = 1.18549 g at 100% efficiency.
With 95%: 1.18549 × 0.95 = 1.1262 g.
Volume 1.1262 ÷ 8.96 = 0.12569 cm³; ÷ 50 cm² = 0.0025139 cm = 25.14 µm.

Each point is the calculator re-run with only “Electrons per ion” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Electrons per ion	Mass deposited (g)
0.5	4.504877896
1	2.252438948
1.5	1.501625965
2	1.126219474
2.5	0.9009755793
3	0.7508129827
4	0.5631097371

How to read the result

The thickness is an average over the area; edges and corners collect more metal than recesses. The deposited mass is proportional to both current and time, so doubling either doubles the mass.

Common mistakes

Entering the area of one side when both sides of a part are plated.
Using the wrong n for the oxidation state in the bath (for example copper from a Cu⁺ cyanide bath has n = 1).
Assuming 100% efficiency for baths that are much less efficient, such as hard chromium.

Keep in mind: Results are theoretical. Real deposits depend on current density limits, bath chemistry, agitation and part geometry; follow the bath supplier's data and safety rules for the chemicals used.

Frequently asked questions

How long does it take to plate a target thickness?

Rearrange: t = (thickness × ρ × A × n × F) ÷ (I × M × efficiency), keeping units consistent.

Does the same formula work for gas evolved at an electrode?

Yes. For hydrogen, 2 electrons give one H₂ molecule, so moles of H₂ = I·t/(2F).

What is a typical current density for copper plating?

It depends strongly on the bath; use the range on the bath's technical sheet rather than a general number.

Sources: M. Faraday, Experimental Researches in Electricity, Seventh Series, Philosophical Transactions of the Royal Society (1834) · CODATA 2018 recommended values, Faraday constant (NIST)

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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