Electrolysis Calculator (Faraday's Law)
Use Faraday's first law of electrolysis to calculate the mass of a substance deposited at an electrode, the charge required, the current needed, or the time to reach a target mass. Choose an element preset or enter custom molar mass and valence values. Include a current efficiency factor for real-world plating processes. The result panel shows moles deposited, total charge in coulombs, and a breakdown chart of mass versus time.
Formula
Worked example
Copper electroplating at 5 A for 1 hour (3600 s) with 95% efficiency: Q = 5 x 3600 = 18,000 C; m = (63.546 x 18,000 x 0.95) / (2 x 96,485) = 5.62 g of copper deposited.
Faraday's Law of Electrolysis
Electrolysis is the process of using an electric current to drive a non-spontaneous chemical reaction, most commonly the deposition of a metal at a cathode or the evolution of a gas. The quantitative relationship between charge and mass was established by Michael Faraday in the 1830s. His first law states that the mass deposited is directly proportional to the total charge (Q) passed through the electrolyte. His second law states that the mass deposited per unit charge is proportional to the molar mass of the substance divided by its valence (the number of electrons transferred per ion). Combined, these give the fundamental formula m = (M x Q x eta) / (n x F), where F = 96,485 C per mole of electrons is the Faraday constant and eta is the current efficiency.
How to use this calculator
Select what you want to solve for using the "Solve for" dropdown. To find the mass deposited, provide current and time. To find the charge needed, enter the target mass. To find the current or time required for a given mass, fill in the target mass and the other variable. Choose an element preset (Silver, Copper, Nickel, Gold, Zinc, Aluminum, and others are included) or select "Custom substance" and enter the molar mass and valence manually. Adjust the current efficiency if your process is not 100% efficient; industrial electroplating baths typically run at 85 to 98%. The results include moles deposited, total charge in coulombs, and the deposition rate in grams per hour. The step-by-step panel shows the full arithmetic with your values substituted in.
Current efficiency and real-world losses
In an ideal electrolysis cell, 100% of the supplied current converts into the target reaction. In practice, competing reactions - most commonly hydrogen evolution at the cathode and oxygen evolution at the anode - consume a fraction of the charge without depositing the desired substance. Current efficiency (eta) is the ratio of actual mass deposited to the theoretical maximum, expressed as a percentage. Setting eta below 100% scales the result accordingly, so the calculator gives the real-world mass rather than the theoretical ideal. For example, at 90% efficiency with 10,000 C of charge, only 9,000 C effectively drives the deposition reaction. Typical values: copper sulfate baths 90-98%, nickel sulfamate baths 95-99%, chromium plating baths 10-25% (most current evolves hydrogen).
Applications of electrolysis
Electrolysis underpins a wide range of industrial and laboratory processes. Electroplating deposits a thin layer of metal onto a substrate to improve appearance, corrosion resistance, or electrical conductivity. Electrorefining purifies metals (most copper is produced this way). Electrolytic production of chlorine and sodium hydroxide (the chlor-alkali process) is one of the largest-scale industrial electrolyses. Water electrolysis splits H2O into hydrogen and oxygen gas, a key route to green hydrogen fuel. Anodizing aluminum grows a controlled oxide layer for durability. Electroforming builds precision metal parts by deposition on a mandrel. In all cases, Faraday's law determines exactly how much charge is needed to produce a given quantity of product.
Common electrolysis element reference
| Element | Symbol | Molar mass (g/mol) | Valence (n) | Common application |
|---|---|---|---|---|
| Silver | Ag+ | 107.868 | 1 | Silverware plating, electronics |
| Copper | Cu2+ | 63.546 | 2 | PCB plating, refining |
| Nickel | Ni2+ | 58.693 | 2 | Corrosion resistance coatings |
| Gold | Au3+ | 196.967 | 3 | Jewelry, electrical contacts |
| Iron | Fe2+ | 55.845 | 2 | Steel production, electroforming |
| Zinc | Zn2+ | 65.38 | 2 | Galvanizing steel |
| Aluminum | Al3+ | 26.982 | 3 | Anodizing, refining (molten) |
| Chromium | Cr3+ | 51.996 | 3 | Hard chrome plating |
| Lead | Pb2+ | 207.2 | 2 | Battery production |
| Hydrogen | H2 | 2.016 | 2 | Water splitting, fuel cells |
| Oxygen | O2 | 31.999 | 4 | Water splitting (anode side) |
Standard molar masses and valence numbers for common electrolysis applications. Faraday constant F = 96,485 C/mol.
Frequently asked questions
What is Faraday's constant and where does it come from?
Faraday's constant (F = 96,485 C/mol) is the charge of one mole of electrons. It is calculated as the elementary charge of a single electron (1.602 x 10-19 C) multiplied by Avogadro's number (6.022 x 10^23 mol-1). Because depositing one mole of a monovalent ion (like Ag+) requires one mole of electrons, F is the charge needed to deposit one mole of a monovalent substance. For divalent ions (like Cu2+), you need 2F, and so on.
How do I convert between coulombs and ampere-hours?
1 ampere-hour (Ah) = 3,600 coulombs (C), because 1 A x 3,600 s = 3,600 C. So 1 mAh = 3.6 C. For example, a 10 Ah capacity represents 36,000 C of charge. To use this calculator with mAh, multiply your mAh value by 3.6 to get coulombs.
What does valence (n) mean in electrolysis?
Valence (also called the ionic charge or number of electrons transferred) is how many electrons are gained or lost per ion during electrolysis. Silver ions (Ag+) have valence 1 because each ion needs 1 electron to become a neutral silver atom. Copper ions (Cu2+) have valence 2, aluminum ions (Al3+) have valence 3. A higher valence means more charge is needed to deposit the same mass.
Why does chromium plating have such low current efficiency?
Chromium electroplating from hexavalent chromium baths is notorious for current efficiencies of only 10 to 25%. The vast majority of the applied current goes toward evolving hydrogen gas at the cathode rather than depositing chromium. Trivalent chromium baths achieve higher efficiency (around 25-50%), and modern research targets even higher values. Always check the current efficiency for your specific chemistry when calculating charge requirements for chromium.
Can I use this calculator for water electrolysis (hydrogen production)?
Yes. Select "Hydrogen gas (H2)" from the element dropdown (molar mass 2.016 g/mol, valence 2). The mass result will be the grams of H2 produced at the cathode. To find the oxygen produced simultaneously at the anode, use molar mass 31.999 g/mol and valence 4. Note that the actual volumes of gas can be calculated from the mass using the ideal gas law at standard conditions (1 mol of any gas at 0 C, 1 atm occupies about 22.4 L).
What is the difference between the first and second laws of electrolysis?
Faraday's first law states that the mass deposited is proportional to the total charge passed (m is proportional to Q). This means doubling the current or doubling the time doubles the mass. Faraday's second law states that for the same charge, the mass deposited is proportional to M/n (molar mass divided by valence). This is why 96,485 C deposits 107.9 g of silver (M/n = 107.9/1) but only 31.8 g of copper (M/n = 63.5/2). Both laws are combined in the single formula m = MQ/(nF).
How accurate is this electrolysis calculator?
The calculator applies Faraday's law exactly, which is theoretically precise for ideal conditions. Real electrolysis cells deviate due to side reactions (addressed by the current efficiency input), concentration overpotential, ohmic resistance, and temperature effects. Use the current efficiency field to account for known losses in your specific process. For research-grade accuracy, measure the actual current efficiency experimentally under your operating conditions rather than assuming 100%.