The electrolysis calculator above applies Faraday's laws of electrolysis, which connect the electric charge passed through a cell to the amount of substance produced at an electrode. Enter a current, a time, a molar mass and the number of electrons in the half-equation, and it returns the mass deposited or released. Switch modes and it solves for the time or the current needed to reach a target mass instead, which is the form the question usually takes when a plating run has to hit a specification.
Arb Digital publishes free calculators for the calculations that are simple in principle and easy to get wrong in practice. Here the trap is the electron count. Depositing a gram of silver takes half the charge of depositing a gram-equivalent of copper because silver transfers one electron and copper transfers two, and a page that hides that variable hides the entire point of Faraday's second law.
What This Electrolysis Calculator Does
It computes the mass of a substance liberated or deposited at an electrode from the charge passed, using the molar mass and the electron count for the relevant half-reaction. The supporting figures give the total charge in coulombs, the moles of electrons that charge represents, the moles of substance produced and, where the product is a gas, the volume that many moles occupies at standard temperature and pressure.
Current efficiency is included as an input because real cells never achieve one hundred percent. Some of the current goes into side reactions, most commonly hydrogen evolution at the cathode in aqueous plating, and the deposited mass falls short of the ideal by exactly that fraction. Leaving efficiency out of the model is the single largest reason a calculated plating time does not match a measured one.
One boundary needs stating clearly, because two different laws share the same name. The live Faraday's law calculator covers Faraday's law of electromagnetic induction, which gives the EMF produced by a changing magnetic flux in a coil. This page covers Faraday's laws of electrolysis, which relate charge to chemical change. They are two unrelated discoveries by the same person, and confusing them is common enough that it is worth saying outright.
How to Use It
- Choose what to solve for. Mass is the default; time and current are the two ways the question is asked in process work.
- Pick a substance preset or select Custom and enter your own molar mass and electron count from the half-equation.
- Enter the current and time, or the target mass if you are solving in the other direction.
- Set the current efficiency. Leave it at 100 for an ideal calculation, or enter a measured value for a real cell.
- Check the moles of electrons in the grid. That figure is charge divided by the Faraday constant and is the quantity every other result derives from.
The Formula and How It Is Calculated
Faraday's first law says the amount of substance produced is proportional to the charge passed. His second says that for a given charge, the amounts of different substances are proportional to their equivalent weights, meaning molar mass divided by electrons transferred. Combined into one expression: m = (Q × M) / (n × F), where Q is the charge in coulombs, M the molar mass in g/mol, n the electrons per formula unit, and F the Faraday constant. Charge itself is Q = I × t, current in amperes times time in seconds.
The Faraday constant is exact under the current SI at 96,485.33212 C/mol, published as the NIST CODATA value for the Faraday constant. It is the elementary charge multiplied by the Avogadro constant, which is why it is exact rather than measured: both of those are now defined values.
Working the default example: 2 amperes for one hour is 7,200 coulombs. Dividing by 96,485.33 gives 0.074623 moles of electrons. Copper deposits as Cu²⁺ + 2e⁻ → Cu, so the moles of copper are half that, 0.037311, and multiplying by 63.546 g/mol gives 2.371 grams. Reversing it, depositing 5 grams of copper needs 5 × 2 × 96,485.33 ÷ 63.546 = 15,183 coulombs, which at 2 amperes takes 7,592 seconds, or about 2 hours 6 minutes. Molar masses used here can be confirmed against the NIST Chemistry WebBook.
Getting the Electron Count Right
Every error of a factor of two or three on this page comes from n. It is not a property of the element; it is a property of the half-equation, and the same element can take different values in different processes. Copper deposited from a copper(II) sulfate bath takes two electrons per atom. Copper deposited from a copper(I) cyanide bath takes one, and the same charge therefore deposits twice as much metal. Iron plated as Fe²⁺ takes two, iron reduced from Fe³⁺ all the way to the metal takes three.
Gases need particular care because the count belongs to the molecule, not the atom. Water electrolysis produces hydrogen by 2H⁺ + 2e⁻ → H₂, so two electrons yield one molecule of H₂, and oxygen by 2H₂O → O₂ + 4H⁺ + 4e⁻, four electrons per molecule of O₂. That two-to-one ratio in electrons is exactly why hydrogen and oxygen come off in a two-to-one volume ratio, which is a useful check that you have set the problem up correctly.
If you are unsure of the half-equation, work it out before using this page rather than guessing at n. For the thermodynamic side of a cell, the Nernst equation calculator handles how electrode potential varies with concentration, and the cell EMF calculator covers the standard potentials of a full cell. Neither affects how much is deposited; they determine whether the reaction runs and at what voltage.
Why Real Cells Fall Short
Faraday's laws are exact. Plating cells are not, and the gap has a name: current efficiency. In an aqueous bath, part of the current reduces hydrogen ions instead of metal ions, particularly at high current density or low metal concentration. Chromium plating is the extreme case, sometimes running below twenty percent efficiency, while acid copper and silver baths can approach one hundred.
Efficiency is a measured property of a specific bath at a specific condition, not a constant you can look up for a metal. It varies with temperature, agitation, pH, additive concentration and current density. That is why a plating line establishes it empirically by weighing a test coupon and comparing against the theoretical mass, which is exactly the calculation this page performs.
Two further practical points. The mass this page returns is the total deposited, distributed over the whole cathode area; thickness follows only if you also know that area and the density of the deposit, and real deposits are thicker at edges and points because current density is not uniform. And the current must be the current actually passing through the cell, not the power supply setting, since a supply in constant-voltage mode delivers whatever current the cell resistance allows. The electrical power calculator covers the supply side of that relationship.
Charge, Coulombs and Ampere-Hours
Charge is the quantity that actually matters, and it appears in several units that people mix up. One coulomb is one ampere for one second. One ampere-hour is 3,600 coulombs. One faraday is 96,485.33 coulombs, which is one mole of electrons. A cell run at 10 amperes for 8 hours passes 80 ampere-hours, which is 288,000 coulombs, or 2.985 faradays.
Thinking in faradays is often the fastest route to a sanity check. If a process needs one mole of product and the half-equation transfers two electrons, it needs two faradays, or about 53.6 ampere-hours, regardless of what the product is. That immediately tells you the scale of the plant: producing a tonne of aluminium, which takes three electrons per atom at 26.98 g/mol, requires roughly 2.98 million faradays, and the enormous current demand of a smelter follows straight from that. The electric charge converter moves between these units, and the battery capacity calculator works in the same ampere-hour terms for storage rather than for synthesis.
Where the Amount Ends Up in a Wider Calculation
The moles figure this page produces is a stoichiometric quantity like any other, and it usually feeds into something else. If you are depositing metal from a solution, the amount removed changes the bath concentration, which the molarity calculator quantifies. If your product is a gas, the volume at STP shown in the grid is a first approximation, and the ideal gas law calculator gives the volume at the actual temperature and pressure of collection, which is usually what you measured. And converting between moles and grams for anything downstream is the job of the moles to grams calculator.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Using the wrong electron count — n comes from the half-equation, not from the element, and copper from a cyanide bath differs from copper from a sulfate bath.
- Leaving time in hours — charge is amperes times seconds, so an hour entered as 1 gives an answer 3,600 times too small.
- Assuming one hundred percent efficiency — aqueous plating baths lose current to hydrogen evolution, sometimes most of it.
- Counting electrons per atom for a diatomic gas — hydrogen needs two electrons per H₂ molecule and oxygen four per O₂ molecule.
- Reading mass as thickness — converting requires the cathode area and the deposit density, and real deposits are not uniform.
Related Free Tools From Arb Digital
For the induction law that shares Faraday's name, see the Faraday's law calculator. The Nernst equation calculator and cell EMF calculator cover the potentials that decide whether a cell reaction proceeds, the electric charge converter handles coulombs and ampere-hours, and the electrical power calculator covers the supply side. For the chemistry that follows, use the moles to grams calculator, the molarity calculator and the ideal gas law calculator. The full free online tools hub lists everything else.
Frequently Asked Questions
The first says the amount of substance produced at an electrode is proportional to the charge passed. The second says that for a fixed charge, the amounts of different substances are proportional to their equivalent weights, meaning molar mass divided by electrons transferred.
The charge carried by one mole of electrons, exactly 96,485.33212 coulombs per mole under the current SI. It is the elementary charge multiplied by the Avogadro constant, both of which are now defined values.
About 2.37 grams at full efficiency. Two amperes for 3,600 seconds is 7,200 coulombs, which is 0.0746 moles of electrons, and copper takes two electrons per atom at 63.546 g/mol.
Take it from the balanced half-equation at the electrode of interest. Cu²⁺ + 2e⁻ → Cu gives two, Ag⁺ + e⁻ → Ag gives one, and 2H₂O → O₂ + 4H⁺ + 4e⁻ gives four per oxygen molecule.
Almost always current efficiency. Part of the current drives side reactions, most often hydrogen evolution at the cathode. Enter a measured efficiency percentage to bring the calculation in line with the bath.
Not directly. It gives the total mass deposited. Thickness also requires the cathode area and the density of the deposit, and real coatings are thicker at edges where current density is higher.
No. Induction relates a changing magnetic flux to an induced voltage in a coil. These are the laws of electrolysis, which relate electric charge to chemical change. They share a name and nothing else.
This calculator is provided for education and general reference. It computes published physical laws from values you supply and is not process, electrical or chemical safety guidance; follow the procedures and risk assessments issued by your own institution or employer.
