Electrolysis Calculator
Calculate the mass, moles, or gas volume deposited or dissolved during electrolysis from current and time, or solve in reverse to find how long a cell must run — with an animated electron-flow diagram, half-reaction picker, and full step-by-step working using Faraday's Law.
Background
Electrolysis uses electrical current to drive a non-spontaneous chemical reaction, typically depositing a metal at the cathode or producing a gas at an electrode. The amount of substance produced depends on how much charge passes through the cell, governed by Faraday's Law: charge Q = I × t, and moles of electrons = Q / F, where F (Faraday's constant) is 96,485 C/mol — the charge carried by one mole of electrons. Each half-reaction requires a specific number of electrons (n) per mole of product, so moles of product = moles of electrons / n.
How to use this calculator
- Choose whether you want to find the amount produced (forward) or the time required to reach a target mass (reverse).
- Pick a common half-reaction — this automatically fills in the electrons per mole (n) and molar mass — or choose Custom to enter your own values.
- Enter current, time (or target mass for reverse mode), and optionally current efficiency and molar gas volume if your product is a gas.
- Click Calculate to see the charge passed, moles of electrons, moles of product, mass or volume, a cell diagram, and the full step-by-step math.
How electrolysis calculations work
Step 1 — Find the charge passed. Charge is current multiplied by time: Q = I × t, measured in coulombs (C). Time must be converted to seconds since current is in amperes (coulombs per second).
Step 2 — Account for efficiency (if given). Real electrolytic cells aren't perfectly efficient — some current is lost to side reactions. Effective charge is Q_eff = Q × (efficiency / 100).
Step 3 — Convert charge to moles of electrons. One mole of electrons carries a fixed charge called Faraday's constant, F = 96,485 C/mol. So moles of e⁻ = Q_eff / F.
Step 4 — Convert moles of electrons to moles of product. Each half-reaction needs a specific number of electrons per mole of product (n). Divide: moles of product = moles of e⁻ / n.
Step 5 — Convert to mass or volume. Multiply moles by molar mass for mass (m = moles × M), or by molar gas volume for volume if the product is a gas (V = moles × Vₘ).
Formula & Equations Used
Charge: Q = I × t (coulombs, with t in seconds)
Effective charge with efficiency: Q_eff = Q × (η / 100)
Moles of electrons: n(e⁻) = Q_eff / F, where F = 96,485 C/mol
Moles of product: n(product) = n(e⁻) / n
Mass: m = n(product) × M
Gas volume: V = n(product) × Vₘ
Reverse-solving for time: t = (target moles × n × F) / (I × η/100)
Example Problems & Step-by-Step Solutions
Example 1 — Mass deposited (Cu²⁺ → Cu)
A current of 2.50 A runs for 30.0 minutes through a copper sulfate solution.
Step 1: Q = 2.50 A × 1800 s = 4500 C
Step 2: moles e⁻ = 4500 / 96,485 = 0.04664 mol
Step 3: moles Cu = 0.04664 / 2 = 0.02332 mol
Result: mass = 0.02332 × 63.546 ≈ 1.48 g of copper deposited.
Example 2 — Gas volume (2H⁺ → H₂ at STP)
A current of 1.20 A runs for 40.0 minutes, producing hydrogen gas at STP (Vₘ = 22.414 L/mol).
Step 1: Q = 1.20 × 2400 = 2880 C
Step 2: moles e⁻ = 2880 / 96,485 = 0.02985 mol
Step 3: moles H₂ = 0.02985 / 2 = 0.01493 mol
Result: volume = 0.01493 × 22.414 ≈ 0.335 L of H₂ gas.
Example 3 — Reverse-solving for time
How long must a 3.00 A current run to deposit 5.00 g of copper (M = 63.546 g/mol, n = 2)?
Step 1: target moles = 5.00 / 63.546 = 0.07867 mol
Step 2: moles e⁻ needed = 0.07867 × 2 = 0.15734 mol
Step 3: charge needed = 0.15734 × 96,485 = 15,180 C
Result: t = 15,180 / 3.00 ≈ 5060 s ≈ 84.3 minutes.
Example 4 — Effect of current efficiency
A cell runs at 2.00 A for 60.0 minutes, but only 90% current efficiency (n=2, M=63.546 for Cu).
Step 1: Q = 2.00 × 3600 = 7200 C
Step 2: Q_eff = 7200 × 0.90 = 6480 C (10% of the charge is "wasted" on side reactions)
Step 3: moles e⁻ = 6480 / 96,485 = 0.06716 mol → moles Cu = 0.03358 mol
Result: mass ≈ 2.13 g — about 10% less than the 2.37 g you'd get at 100% efficiency.
Frequently Asked Questions
What value should I use for n?
Use the number of electrons transferred per mole of product, taken directly from the balanced half-reaction. For example, Cu²⁺ + 2e⁻ → Cu needs n=2, while Ag⁺ + e⁻ → Ag needs n=1. The half-reaction picker fills this in automatically for common species.
Why does time need to be in seconds?
Current (amperes) is defined as coulombs per second, so the charge formula Q = I × t only gives the correct units (coulombs) when t is in seconds. Entering time in minutes or hours without converting is one of the most common errors in electrolysis problems — this calculator converts automatically.
What is current efficiency and why isn't it always 100%?
In a real electrolytic cell, not all of the current goes toward producing your target species — some is lost to side reactions, such as competing reduction/oxidation processes or heat. Current efficiency expresses what fraction of the total charge actually contributes to the desired product.
Do I need molar mass for every calculation?
Only if you want a final answer in grams. If you only need moles of product, you can leave molar mass blank. For gas products, you can instead supply a molar gas volume (e.g., 22.414 L/mol at STP) to get volume instead of, or in addition to, mass.
How does reverse-solving for time work?
Instead of starting from current and time to find mass, reverse mode starts from a target mass, converts it to moles, then to moles of electrons needed, then to total charge required, and finally divides by current to get the time needed — effectively running the whole forward calculation backward.
Why is Faraday's constant 96,485 C/mol?
This is the magnitude of charge carried by one mole of electrons, calculated as Avogadro's number (6.022×10²³) multiplied by the charge of a single electron (1.602×10⁻¹⁹ C). It's one of the fundamental physical constants linking the macroscopic world of measurable current to the microscopic world of individual electrons.
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