Faradaic efficiency calculator for gas and liquid products
Faradaic efficiency is the fraction of the charge passed that ends up in a product: FE = z·n·F / Q, with z the electrons per molecule, n the moles of product, F = 96 485 C/mol and Q the charge. For a gas product measured on-line by GC, the moles come from its volume fraction x in the outlet flow v, so FE = z·F·x·v·p / (R·T·I), with I the total current.
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At a glance
| Formula | FE = z·n·F / Q; gas by GC: z·F·x·v·p / (R·T·I) |
|---|---|
| Constants | F = 96 485 C/mol, R = 8.314 J/(mol·K) |
| Products | H₂, O₂, CO, HCOOH, CH₄, NH₃ (electron counts cited) or any z |
| Input | GC ppm or %, flow rate, current; or moles and charge |
| Output | FE per product, total, production rates; CSV |
| Runs in | Your web browser; nothing is uploaded |
| Price | Free, no account needed |
What it does
How to use the faradaic efficiency calculator
- Choose the methodGas products by GC (on-line measurement in the outlet stream) or from moles and charge (for liquids or collected gas).
- Enter the cell conditionsGC: total current, outlet gas flow, pressure and temperature. Moles: the charge, or a constant current and the time.
- Add the productsPick each product (its electron count fills in) and enter its GC concentration or amount; use “Other” to type any z.
- Read the efficienciesRead the Faradaic efficiency of each product, the total, and how much of the charge is not in the products entered.
- ExportCopy the results or download them as CSV.
How it works
Faraday’s law links charge and product: making one molecule takes z electrons, so n moles take z·n·F coulombs. The Faradaic efficiency is that charge as a fraction of the charge Q actually passed (Small 2026, doi:10.1002/smll.74606):
FE = z·n·F / Q
with F = 96 485 C mol⁻¹ and Q from the integrated chronoamperogram, or current × time at constant current. It is the ratio of the product found to the product expected at 100 % Faradaic efficiency (doi:10.1039/d1ra08530a).
Gas products by GC. For a product measured on-line in the outlet gas (ACS Appl Energy Mater 2025, doi:10.1021/acsaem.5c01865):
FE = z·F·x·v·p / (R·T·I)
where x is the volume fraction of the product (ppm × 10⁻⁶), v the outlet gas flow rate in m³/s, p the pressure (101.325 kPa), R = 8.314 J mol⁻¹ K⁻¹, T the gas temperature in K, and I the total current. The term x·p·v / RT is the product’s molar flow by the ideal gas law. Use the flow leaving the cell at the T and p you enter.
Electrons per molecule. Two for H₂ and four for O₂ (the two-electron HER and four-electron OER, doi:10.3390/nano12132209); two for CO and for formic acid from CO₂ (doi:10.1021/acs.accounts.4c00283); eight for CH₄ from CO₂ (doi:10.1002/anie.202508497); eight for NH₃ from nitrate (doi:10.3390/molecules31132307). For other products type z yourself.
For the reaction figures to go with the numbers, see the electrocatalysis templates.
Worked example
CO₂ reduction, GC. A cell runs at 100 mA with an outlet gas flow of 20 mL/min at 25 °C and 101.325 kPa. The GC finds 18 000 ppm CO, 3500 ppm H₂ and 400 ppm CH₄. For CO, the molar flow is 0.018 × 101 325 Pa × 3.333 × 10⁻⁷ m³/s / (8.314 × 298.15) = 2.45 × 10⁻⁷ mol/s (883 µmol/h), and FE = 2 × 96 485 × 2.45 × 10⁻⁷ / 0.100 = 47.3 %. H₂ gives 9.2 % and CH₄ (z = 8) 4.2 %, 60.7 % in total; the other 39.3 % of the charge went to products not measured here (liquids, for example) or was lost.
Water electrolysis, moles. 10 mA for one hour passes 36 C. Finding 120 µmol of H₂ gives FE = 2 × 120 × 10⁻⁶ × 96 485 / 36 = 64.3 %.
Frequently asked questions
How do you calculate Faradaic efficiency?
Divide the charge that went into the product by the charge passed: FE = z·n·F / Q, with z the electrons per molecule, n the moles of product, F = 96 485 C/mol and Q the total charge in coulombs.
How do I calculate Faradaic efficiency from GC data?
For a gas product in the outlet stream, FE = z·F·x·v·p / (R·T·I): x is its volume fraction (ppm × 10⁻⁶), v the outlet flow rate in m³/s, p the pressure, T the gas temperature and I the total current.
How many electrons are needed for each product?
Two for H₂, four for O₂, two for CO and for formate from CO₂, eight for methane from CO₂ and eight for ammonia from nitrate. For other products enter z yourself.
Why do my Faradaic efficiencies not add up to 100 %?
Some charge may go into products you did not measure (liquid products when only the gas is analysed, for example), into side reactions, or be lost. A total above 100 % usually means a wrong electron count, flow rate or unit.
Which flow rate should I use?
The gas flow leaving the cell, at the pressure and temperature you enter, because the GC concentration refers to that stream.
What charge should I use?
The total charge over the electrolysis, from the integrated chronoamperogram (absolute value), or current × time if the current was constant.
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