Electroplating Mass Calculator

Calculate mass deposited, plating time, and current for electroplating using Faraday's laws of electrolysis.

Current I (A) (A)

Time t (s) (s)

1 hour = 3600 s

Molar mass M (g/mol) (g/mol)

Cu=63.5, Ni=58.7, Ag=107.9, Au=197

Electrons transferred n

Cu2+ to Cu: n=2, Ag+ to Ag: n=1

Current efficiency eta (%) (%)

Please check your inputs and try again.

How Faraday’s Laws Work

Electroplating is stoichiometry with electrons as a reagent. Faraday’s insight was that the amount of substance deposited is directly proportional to the charge passed, and that the proportionality depends only on the molar mass and how many electrons each ion needs.

m = (M × I × t × η) / (n × F)

Symbol	Meaning	Units / value
m	Mass deposited	g
M	Molar mass of the metal	g/mol
I × t	Total charge passed	A × s = coulombs
n	Electrons per ion reduced	2 for Cu²⁺, 1 for Ag⁺, 3 for Au³⁺
F	Faraday constant	96,485 C/mol — charge on one mole of electrons
η	Current efficiency	Fraction of current doing useful plating

The Faraday constant is simply Avogadro’s number multiplied by the elementary charge. It is the bridge between the electrical world of coulombs and the chemical world of moles, which is why it appears in every electrolysis calculation.

The n term explains a common surprise: plating silver requires only one electron per atom, while gold from Au³⁺ requires three. Per coulomb of charge you therefore deposit three times as many silver atoms as gold atoms, before molar mass is even considered.

Why Efficiency Is Below 100%

Loss mechanism	What happens	Typical impact
Hydrogen evolution	Water reduced to H₂ instead of metal ions	Largest single loss in aqueous baths
Side reactions	Impurities or additives reduced at the cathode	Varies with bath cleanliness
Poor current distribution	Deposition uneven across complex shapes	Significant for intricate parts
Bath depletion	Local metal ion concentration falls at the surface	Worse at high current density

Efficiencies of 90–98% are common in well-maintained baths. Chromium plating is a notable exception, often running below 20%, because hydrogen evolution competes heavily — which is why chrome plating consumes so much energy per gram deposited.

Worked Examples

Example 1: Copper plating: I=2A, 1hr, M=63.5, n=2

m=63.5x2x3600/(2x96485)

Result: 2.38g theoretical, 2.14g at 90%

Standard electroplating

Example 2: Silver plating: I=1A, 600s, n=1

m=107.9x1x600/96485

Result: 0.671g theoretical

Jewelry plating

Example 3: Gold plating, three electrons

Au³⁺, M=197, I=0.5 A, t=1800 s, n=3

Result: m = 197 × 0.5 × 1800 / (3 × 96485) = 0.613 g

Gold’s high molar mass is partly offset by needing three electrons per atom, so the deposit is smaller than the atomic weight alone suggests.

Example 4: Solving for time

Deposit 5.00 g of nickel, M=58.7, n=2, I=3 A, η=95%

Result: t = (5.00 × 2 × 96485)/(58.7 × 3 × 0.95) = 5,768 s ≈ 96 min

Rearranging for time is the common industrial use — the target thickness is known and the schedule follows.

Example 5: Low-efficiency process

Chromium plating at 18% current efficiency

Result: Over 80% of the electrical energy produces hydrogen, not chrome

This is why decorative chrome is energy intensive and why the calculated theoretical mass is so far from reality without the efficiency term.

Common Mistakes

⚠️

Forgetting the electron count n

Copper from Cu²⁺ needs two electrons per atom while silver from Ag⁺ needs one. Omitting n or using the wrong value gives an answer wrong by a whole factor.

⚠️

Using the wrong oxidation state

The same metal can plate from different ions. Copper from Cu⁺ uses n = 1 while from Cu²⁺ it uses n = 2, halving the mass for the same charge. The bath chemistry determines which applies.

⚠️

Ignoring current efficiency

Theoretical mass assumes every electron reduces a metal ion. Real baths lose current to hydrogen evolution and side reactions, so actual deposits are always lighter than calculated.

⚠️

Mixing time units

The formula requires seconds, since amperes are coulombs per second. Entering hours or minutes without converting inflates the result by 3,600 or 60 times.

Frequently Asked Questions

Faraday's two laws?

1st: mass proportional to charge Q=It. 2nd: mass proportional to equivalent weight M/n. Combined: m=MIt/nF.

Why efficiency <100%?

Side reactions (H2 evolution, O2 evolution) compete with metal deposition. Optimize bath chemistry for high efficiency.

What is Faraday’s constant?

96,485 coulombs per mole — the charge carried by one mole of electrons. It equals Avogadro’s number times the elementary charge, and links electrical charge to moles of substance.

Why does the electron count matter?

Each metal ion needs a specific number of electrons to be reduced. Cu²⁺ needs two, Ag⁺ needs one, Au³⁺ needs three. The same charge therefore deposits different molar amounts.

Why is current efficiency less than 100%?

Some current reduces water to hydrogen rather than metal ions, and some is lost to side reactions and uneven current distribution. Well-run baths reach 90–98%; chromium plating can be under 20%.

How do I calculate plating time for a target mass?

Rearrange to t = (m × n × F) / (M × I × η). This is the usual industrial form, since the required thickness is known in advance.

Do I use seconds or hours?

Seconds. An ampere is one coulomb per second, so time must be in seconds for the units to resolve. Using hours overstates the mass by a factor of 3,600.

Formula Explorer connections

Interpretation: This formula links electron transfer, charge, potential, current or ionic transport in an electrochemical system. Assumption: Balance electron count and half-reactions, preserve sign conventions, and use consistent concentration, temperature and electrical units. Real cells include losses and overpotential.

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