Electrolysis Calculator

Electrolysis moves matter with electricity, and this calculator converts between the two: tell it the current you passed and how long you passed it, and it returns the mass of metal or gas that appeared at one electrode. It also runs the other way, so a target mass can be turned back into the charge, the current or the plating time.

The tool answers three related questions that keep coming up at the bench and on the shop floor.

• How much will I deposit? Give a current and a duration — or a measured charge — and read the mass of the substance you selected.
• How long do I have to run it? Give the target mass and the current your rectifier can hold, and the time is solved for you.
• What is this substance worth electrochemically? Weigh the deposit you actually obtained, enter the charge that produced it, and switch the element menu to Custom: the calculator returns the equivalent you measured.

The mass is the amount moved at one electrode. In a plating tank the workpiece is the cathode and gains that mass, while an anode of the same metal dissolves to replace it, so the bath keeps its composition. Britannica's description of the plating circuit states the same three parts — the article as cathode, an anode of the same metal, and a low-voltage current depositing the metal from solution. Which electrode you care about depends on the job; the arithmetic is the same either way.

You do not need the cell voltage for any of this: the calculation is about charge, not about driving force. Whether the reaction runs at all at your applied voltage is a separate question, and the cell EMF calculator works that side out from the electrode potentials.

Every run is the same four moves. The example below is a real copper plating job: 2 amperes for half an hour.

Copper plating: 2 A for 30 minutes

Copper's tabulated equivalent is $Z_{\mathrm{Cu}} = 3.295\times 10^{-7}\ \mathrm{kg/C}$. Thirty minutes is 1,800 seconds, so the charge is 3,600 coulombs:

So the part gains about 1.19 grams of copper, and a soluble copper anode loses the same amount. Left in milligrams the box reads 1,186.2 mg, which is the same number with the decimal point moved.

The calculator is a direct implementation of Faraday's first law of electrolysis, combined with the definition of electric charge.

$m$ is the mass deposited or dissolved at the electrode, $Q$ is the charge that passed, and $Z$ is the electrochemical equivalent of the substance: the mass one coulomb moves, in kilograms per coulomb. Charge itself is current multiplied by time, which is the second half of the model:

Substitute one into the other and the whole calculator collapses into a single statement, which is why any three of the four quantities determine the remaining one:

The reverse forms are the ones you reach by leaving a box empty: $Q = \frac{m}{Z}$, $t = \frac{m}{Z\,I}$, $I = \frac{m}{Z\,t}$, and — under Custom — $Z = \frac{m}{Q}$.

Where the tabulated constants come from

Each equivalent in the Element menu is built from the substance's molar mass and the number of electrons its ion exchanges:

$M$ is the molar mass in kilograms per mole, $n$ is the number of electrons the species exchanges (2 for a copper ion, 1 for a silver ion, 4 for an oxygen molecule), and $F$ is the Faraday constant, 96 485.332 12 C/mol on the NIST reference values. Copper illustrates it: a molar mass of 0.06355 kg/mol divided by twice that constant gives 3.29 × 10⁻⁷ kg/C, and the Element menu carries 3.295 × 10⁻⁷ kg/C — the same figure rounded to the four significant digits the table prints. Because the same charge always moves the same number of electrons, doubling $n$ halves the deposit — that is the practical content of Faraday's second law.

If you need the molar mass of something that is not in the Element menu, the molar mass calculator gives you $M$ to drop into the formula above.

What one ampere hour actually deposits

The spread is worth noting: one ampere hour buys a few grams of copper or silver but only 0.038 g of hydrogen, because hydrogen is the lightest element that an electrode can release with one electron per atom.

Units are normalised before the formula runs

Every menu is converted into the base unit first — coulombs, seconds and kilograms — so mixing units can never corrupt the arithmetic. A charge typed as 4,000 mAh enters the equation as 14,400 C; a time typed as 30 min enters as 1,800 s; a mass typed as 5 g enters as 0.005 kg.

Three runs that behave differently: a normal plating job, a battery driving water electrolysis, and a reverse solve for a target mass.

The arithmetic is exact for the charge you enter; the interesting part is whether the charge you enter is the charge that did the work.

• The number is a magnitude for one electrode. In a plating cell the workpiece (cathode) gains it and the matching anode loses it. The calculator tracks how much matter moves, not which way the current flows.
• Zero current means a genuine zero. Set the current to 0 A with a real duration and the result is 0 C and 0 g — an answer, not an error.
• An impossible combination is reported, not faked. A nonzero charge with 0 A cannot be spread over any time, so the time box stays empty and explains why instead of printing an infinite duration. Likewise a run that would need more than a century is flagged, because that means one of the inputs is at the wrong scale.

• It assumes every coulomb goes into the deposit. Real baths divert part of the charge into side reactions such as hydrogen evolution, and the share that ends up in the coating varies widely between processes, baths and current densities — some metals are known for running far below their theoretical rate. Treat the calculated mass as the ceiling that charge could deliver, and compare it with a weighed test coupon before you rely on it.
• Mass is not thickness. A coating's thickness needs the plated area and the metal's density:
  $$t = \frac{m}{\rho\,A}$$
  with $m$ from this calculator, $\rho$ the density of the coating metal and $A$ the area that actually saw current. There is no area field here, so thickness is a step you take outside the tool.
• Small deposits hide in the units. 1.19 g and 1,186 mg are the same result; so are 4,000 mAh and 14,400 C. When comparing against a supplier's specification, convert to one common unit first — mixing the two is the most common way to be a factor of 3,600 out.