Faraday Law Calculator

Faraday's laws of electrolysis describe the quantitative relationship between the amount of substance produced or consumed at an electrode and the quantity of electric charge passed through the electrolyte. Michael Faraday published these laws in the 1830s after meticulous experiments measuring how different electrolytes respond to electric current. They remain the foundation of electrochemistry, electroplating, and industrial electrolytic processes.

The first law states that the mass of a substance deposited or dissolved at an electrode is directly proportional to the total electric charge (Q) that passes through the solution. In formula terms, m ∝ Q, where Q = I × t (current times time). Doubling the current or doubling the electrolysis time doubles the amount of material deposited, all else being equal.

The second law adds that when the same charge passes through different electrolytes, the masses deposited are proportional to their equivalent weights (the molar mass divided by the number of electrons transferred per formula unit, M/n). For example, passing the same charge through silver nitrate and copper sulfate deposits different masses because silver requires one electron per atom (n = 1) while copper requires two (n = 2). These two laws combine into the master equation used in this calculator:

m = (M × I × t) / (n × F)

where M is the molar mass, I is the current in amperes, t is the time in seconds, n is the number of electrons transferred, and F is the Faraday constant (96,485 coulombs per mole of electrons). This single equation lets you solve for any one of the four variables — mass, current, time, or molar mass — when the other three are known.

The calculator implements Faraday's law in three different modes, each solving for a different unknown. The central equation relates four quantities through the Faraday constant.

This calculator supports three calculation modes to solve for any unknown in Faraday's law. Follow the steps below depending on what you need to find:

1. Select a Substance: Choose from 16 common elements and gases including copper, silver, gold, zinc, iron, aluminum, and hydrogen. Each substance automatically loads its molar mass (M) and electron transfer number (n).
2. Choose Calculation Mode: Select "Mass" to find the mass deposited, "Time" to find how long electrolysis takes, or "Current" to find the required current.
3. Enter Known Values: Fill in the two or three known quantities. The current input field is shown unless you are solving for current, and similarly for time and mass. Time can be entered in seconds, minutes, or hours.
4. Read the Results: The calculator displays the answer along with the total charge (Q), moles of substance, and a complete step-by-step calculation breakdown. The results also show the molar mass and electron count used.

The charge Q = I × t is always computed first, then converted to moles via n = Q / (n × F), and finally to mass via m = n × M. This three-step chain is transparent in the result display.

The results panel shows several related quantities that together tell the full story of the electrolysis. The primary answer — mass deposited, time required, or current needed — appears at the top with appropriate units.

Charge (Q) is the total electrical energy passed through the system, measured in coulombs. One coulomb is the charge of approximately 6.24 × 10¹⁸ electrons. A current of one ampere for one second delivers exactly one coulomb.

Moles shows how many moles of the substance correspond to the calculated charge. This connects the electrical measurement to the chemical amount. The relationship is moles = Q / (n × F), where n × F gives the charge needed for one mole of substance.

The calculator also displays the Faraday constant (F = 96,485 C/mol) and the electron count (n) for reference. These values are fixed properties of electrochemistry and do not change with your inputs. The complete calculation breakdown at the bottom of the results lets you verify each arithmetic step.

Faraday's law is the backbone of the electroplating industry, which deposits thin layers of gold, silver, nickel, or chromium onto surfaces for corrosion protection, decorative finishes, and electronic components. The jewelry industry plates gold onto base metals using precisely controlled current and time to achieve desired coating thicknesses. The formula allows engineers to calculate exactly how much gold is needed per batch.

Aluminum production relies entirely on electrolysis. The Hall-Héroult process passes enormous currents (hundreds of thousands of amperes) through molten aluminum oxide dissolved in cryolite. Faraday's law determines the production rate: a cell running at 100,000 A deposits approximately 0.336 kg of aluminum per hour. Understanding these calculations is essential for optimizing energy consumption and production efficiency.

Rechargeable batteries, electrorefining of metals, and chlor-alkali production all rely on Faraday's law. Electric vehicles depend on the reversible electrochemistry described by these principles. In analytical chemistry, coulometric titrations use Faraday's law to determine unknown concentrations by measuring the charge needed to complete a reaction. The law also underpins water purification through electrocoagulation and the production of hydrogen fuel through water electrolysis.