Last updated: July 3, 2026
Electrolysis Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The electrolysis calculator uses Faraday's laws to compute electrode mass from current, time, molar mass, and electron count. It also reports charge, moles of electrons, moles deposited, and can rearrange the same relation to estimate time or current for a desired target mass.
Mass deposited during electrolysis equals current times time times molar mass divided by electron count times the Faraday constant. In symbols, m equals I t M over n F.
Key Takeaways
- Electrolysis mass follows m = Q×M/(n×F), with charge Q = I×t.
- One Faraday, 96485 C, corresponds to one mole of electrons transferred.
- Copper(II) plating uses n = 2, while silver(I) plating uses n = 1.
- The same equation rearranges to find required time or current for a target mass.
- Real plated mass can be lower than theory when current efficiency is less than 100%.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
m = (Q·M)/(n·F), Q = I·t
Where:
- m=Mass deposited or liberated at the electrode(g)
- Q=Total electric charge passed(C)
- I=Electric current(A)
- t=Electrolysis time(s)
- M=Molar mass of the deposited substance(g/mol)
- n=Electrons transferred per ion or formula unit(mol e⁻/mol substance)
- F=Faraday constant(C/mol e⁻)
Worked Examples
Copper electroplating at 2 A for 1 hour
Copper(II) ions gain two electrons per copper atom, so n = 2.
- 1Calculate charge: Q = I × t = 2 A × 3600 s = 7200 C.
- 2For Cu²⁺ + 2e⁻ → Cu, use M = 63.55 g/mol and n = 2.
- 3Apply m = Q×M/(n×F) = 7200×63.55/(2×96485).
- 4The deposited copper mass is 2.371 g; the electron amount is Q/F = 0.0746 mol e⁻.
Silver electroplating at 1 A for 1 hour
Silver(I) needs one electron per silver atom, so the same charge deposits more mass than copper.
- 1Calculate Q = 1 A × 3600 s = 3600 C.
- 2For Ag⁺ + e⁻ → Ag, use M = 107.87 g/mol and n = 1.
- 3Apply m = 3600×107.87/(1×96485).
- 4The result is 4.025 g of silver deposited.
Copper run with Q = 9650 C
A 5 A copper-plating run lasting 1930 s passes about one tenth of a mole of electrons.
- 1Calculate Q = 5 A × 1930 s = 9650 C.
- 2Use m = Q×M/(n×F) with M = 63.55 g/mol and n = 2.
- 3m = 9650×63.55/(2×96485) = 3.178 g.
- 4Moles of electrons are 9650/96485 ≈ 0.100 mol e⁻.
Time needed to plate 1 g of copper
Rearrange Faraday's law to solve plating time when current is fixed.
- 1Rearrange m = I×t×M/(n×F) to t = m×n×F/(I×M).
- 2Substitute m = 1 g, n = 2, F = 96485 C/mol, I = 2 A, and M = 63.55 g/mol.
- 3t = 1×2×96485/(2×63.55) = 1518.3 s.
- 4That is about 25.3 minutes of ideal 100% current-efficient plating.
Introduction
The electrolysis calculator applies Faraday's laws to estimate how much material is deposited or liberated at an electrode when a known current flows for a known time. The central relation is m = Q×M/(n×F), where charge is Q = I×t, molar mass is M, electron stoichiometry is n, and the Faraday constant is 96485 C/mol. It is designed for common electroplating contexts such as copper and silver, and pairs naturally with the cell EMF calculator and Nernst equation calculator when you also need voltage and concentration effects.
Faraday's law formula for electrode mass
For an ideal electrolytic cell, the charge delivered to an electrode is Q = I×t. One mole of electrons carries one Faraday of charge, so the moles of electrons are Q/F. If each ion needs n electrons to form one mole of neutral product, moles deposited are Q/(nF), and mass is m = Q×M/(nF). This calculator reports all three quantities so you can check the charge balance behind the mass result.
Choosing molar mass M and electron count n
The electron count comes from the balanced half-reaction. For copper electroplating, Cu²⁺ + 2e⁻ → Cu, so n = 2 and M ≈ 63.55 g/mol. For silver, Ag⁺ + e⁻ → Ag, so n = 1 and M ≈ 107.87 g/mol. Use the molar mass calculator or atomic mass calculator to verify the mass term for less familiar products.
Copper electroplating worked example
Suppose a copper bath runs at 2.00 A for 1.00 h. The charge is 2×3600 = 7200 C. With M = 63.55 g/mol, n = 2, and F = 96485 C/mol, Faraday's law gives m = 7200×63.55/(2×96485) = 2.371 g of copper. The same setup transfers 7200/96485 = 0.0746 mol of electrons and deposits half that amount, 0.0373 mol, of copper atoms.
Silver plating and current efficiency
A 1.00 A silver-plating run for 1.00 h passes 3600 C. Because Ag⁺ needs only one electron, m = 3600×107.87/96485 = 4.025 g. Real plating may be lower if hydrogen evolution, side reactions, poor contact, or incomplete current efficiency consume part of the charge. For practical electrochemistry context, see the LibreTexts electrolysis chapter/17%3A_Electrochemistry/17.07%3A_Electrolysis).
Solving time or current for a target mass
Faraday's law can be rearranged. To find time, use t = m×n×F/(I×M). To find current, use I = m×n×F/(t×M). For example, depositing 1.00 g of copper at 2.00 A takes 1×2×96485/(2×63.55) = 1518.3 s, about 25.3 min. If you prepare solutions by mass or amount first, companion tools such as the mole calculator and grams to moles calculator help set up the bath composition.
Assumptions and limits
The calculation assumes 100% current efficiency, constant current, correct electron stoichiometry, and complete deposition at the chosen electrode. It does not model overpotential, electrode area, stirring, concentration depletion, competing gas evolution, or changing activity. Definitions and constants can be cross-checked in the IUPAC Gold Book and the NIST constants database.
Quick Reference Card
Electrolysis — Quick Reference
Quick reference • Electrolysis Calculator
Q = I×t; m = Q×M/(n×F); F = 96485 C/mol e⁻Valid range: Use positive current, time, molar mass, and electron count; best for ideal 100% current-efficiency electrolysis.
Common Values
⚠ Watch Out
- •Use seconds for time; hours must be multiplied by 3600.
- •Use the electron count from the balanced half-reaction, not from the overall equation alone.
- •Do not expect theoretical mass if gas evolution or other side reactions consume current.
- •Keep current positive and use the average current for non-constant-current runs.
Pro Tips
- →Compute Q first; it makes charge, moles of electrons, and mass easy to audit.
- →For plating thickness, divide the mass by density and plated area after this calculation.
- →Check units: A×s equals coulombs, and g/mol keeps the final mass in grams.
- →Use target-mass solving to plan plating time before starting a constant-current run.
FAQs
How do I calculate mass deposited during electrolysis?
Calculate charge as Q = I×t, then use m = Q×M/(n×F), where M is molar mass, n is the electron count in the half-reaction, and F = 96485 C/mol.
What value of n should I use for copper electroplating?
For the common Cu²⁺ + 2e⁻ → Cu half-reaction, use n = 2. If the half-reaction or oxidation state is different, balance it and use the corresponding number of electrons.
Why does silver deposit more mass than copper for similar charge?
Silver has a larger molar mass and Ag⁺ needs only one electron, while Cu²⁺ needs two electrons. Both factors increase the silver mass per coulomb.
Can this calculator solve the time needed for a target mass?
Yes. Enter target mass, current, molar mass, and electron count, set time to zero if needed, and use solveFor = time in programmatic calls. The rearranged relation is t = m×n×F/(I×M).
Can this calculator solve the current needed?
Yes. Enter target mass, time, molar mass, and electron count, and use solveFor = current in programmatic calls. The rearranged relation is I = m×n×F/(t×M).
Why can real plated mass be lower than the calculated mass?
Faraday's law gives the theoretical mass for 100% current efficiency. Side reactions, hydrogen evolution, poor contact, passivation, or inaccurate current measurement can reduce actual deposited mass.