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Electrolysis Calculator

Ready to calculate
Faraday's First Law.
12 Species + Custom.
Auto Z = M/(n·F).
100% Free.
No Data Stored.

How it Works

01Pick the Element

12 common species (Ag, Cu, Ni, Au, Fe, Zn, H₂, Na, K, O₂, Al) auto-fill Z = M / (n·F).

02Enter Current I

DC current through the cell in amps, mA, or kA. Constant-current operation assumed.

03Enter Time t

Duration in seconds, minutes, hours, or days. Charge Q = I × t.

04Get Mass Deposited

Faraday's first law: m = Z × Q. Output in g, kg, or mg with energy / power summary.

What is an Electrolysis Calculator?

Electrolysis — driving a non-spontaneous redox reaction with an external electric current — is the foundation of industrial-scale metal production (aluminum, copper, zinc, sodium, magnesium), electroplating (decorative chrome, gold-plated electronics), water-splitting hydrogen generation, and dozens of analytical-chemistry techniques. Our Electrolysis Calculator implements Michael Faraday's First Law of Electrolysis (1834), the cornerstone equation of electrochemistry: m = Z × Q = Z × I × t, where m is the mass deposited at the electrode, Z is the electrochemical equivalent (kg/C), Q is the total charge passed (C), I is the current (A), and t is the time (s).

The electrochemical equivalent Z is computed from the element-and-half-reaction-specific formula Z = M / (n × F) where M is the molar mass (g/mol), n is the number of electrons transferred per ion (the valency), and F is the Faraday constant (96,485 C/mol — the charge of one mole of electrons). The calculator auto-fills Z for 12 common species spanning the most-deposited metals and gases in industry and chemistry teaching: Silver (Z = 1.118 µg/C, the historical "silver coulometer" reference), Copper (3.29 µg/C, the most-deposited metal globally — annual industrial Cu electrowinning ~5 million tonnes), Nickel (3.04 µg/C, matching the screenshot example of 3.04×10⁻⁷ kg/C), Gold, Iron, Zinc, Hydrogen, Sodium, Potassium, Oxygen, Aluminum, plus a Custom mode for any species not in the list.

Output gives theoretical mass deposited at 100% current efficiency in g / kg / mg, total charge passed in C / kC / Ah, moles of metal deposited (Q/(n·F)), and a theoretical energy estimate based on the standard reduction potential E0 — useful for sizing electroplating baths, electrowinning cells, hydrogen-generation electrolyzers, and electrochemistry teaching demonstrations. Designed for electrochemistry students, electroplating shops, electrowinning process engineers, hydrogen-economy / clean-energy engineers, and analytical chemistry coulometry workflows, the tool runs entirely in your browser — no account, no data stored.

Pro Tip: Pair this with our Serial Dilution Calculator for analytical-chemistry standard preparation, our Buffer pH Calculator for electrolyte preparation, or our Molarity Calculator for electrolyte stock preparation.

How to Use the Electrolysis Calculator?

Pick the Element to Be Deposited: 12 common species cover most teaching and industrial cases (Ag, Cu, Ni, Au, Fe, Zn, H₂, Na, K, O₂, Al). Each auto-fills its Z value computed from M / (n × F). For species not in the list, pick "Custom" and enter Z directly in kg/C.
Verify the Electrochemical Constant Z: The auto-filled value uses IUPAC atomic masses and the standard valency for the most common deposition reaction (e.g. Cu²⁺ + 2e⁻ → Cu uses n = 2). For unusual oxidation states (e.g. Cu⁺ for cuprous baths instead of Cu²⁺), use Custom mode with Z = M/(n·F) computed for your specific reaction.
Enter the Cell Current: DC current through the cell in mA, A, or kA. Constant-current operation is assumed; if your cell has variable current, integrate ∫I dt over the operating period to get the total charge Q, then use Q = I × t with effective average I.
Enter the Operating Time: Seconds, minutes, hours, or days. The calculator multiplies I × t internally to get the total charge Q in coulombs.
Apply Faraday's First Law m = Z × Q: The calculator computes m = Z × I × t = (M / (n × F)) × I × t and renders mass in the cleanest unit (µg, mg, g, kg). Also computes moles deposited = Q / (n × F).
Read Mass + Charge + Energy: Theoretical mass at 100% efficiency, charge in C and Ah, moles of metal deposited, and a theoretical energy estimate based on the standard reduction potential E0. Real cells need 2-5× more energy due to overpotentials, IR drop, and concentration polarization.

How is mass deposited calculated?

Faraday's First Law of Electrolysis (1834) is one of the bedrock quantitative results in electrochemistry — the mass of substance deposited or liberated at an electrode is directly proportional to the total charge passed through the cell. The proportionality constant is the electrochemical equivalent, Z, which depends on the element, its valency, and the Faraday constant.

Source: Faraday, M. (1834). "Experimental Researches in Electricity, Seventh Series." Philosophical Transactions of the Royal Society of London, 124. Modern formalisation in CRC Handbook of Chemistry and Physics, IUPAC Quantities, Units and Symbols in Physical Chemistry.

Faraday's First Law

For an electrolysis cell with constant current I (A) operated for time t (s):

Q = I × t    (total charge in coulombs)

m = Z × Q = Z × I × t    (mass deposited in kg)

n = Q / (z × F)    (moles deposited; z = ion valency, F = 96,485 C/mol)

Electrochemical Equivalent Z

Z is element-and-reaction-specific:

Z = M / (n × F)    (kg per coulomb)

where M is the molar mass (kg/mol — note: convert from g/mol by dividing by 1000), n is the valency (electrons transferred per ion), and F = 96,485 C/mol is the Faraday constant.

For Nickel: M = 58.69 g/mol = 0.05869 kg/mol; n = 2 (Ni²⁺ + 2e⁻ → Ni); Z = 0.05869 / (2 × 96485) = 3.04 × 10⁻⁷ kg/C = 0.000000304 kg/C.

Electrochemical Equivalents — Common Species

  • Silver (Ag⁺ + e⁻ → Ag): M = 107.87 g/mol, n = 1, Z = 1.118 × 10⁻⁶ kg/C = 1.118 mg/C. The historical "silver coulometer" used Z(Ag) as the reference standard for measuring charge.
  • Copper (Cu²⁺ + 2e⁻ → Cu): Z = 3.294 × 10⁻⁷ kg/C = 0.3294 mg/C. Most-deposited metal industrially; ~5 million tonnes/yr globally.
  • Nickel (Ni²⁺ + 2e⁻ → Ni): Z = 3.04 × 10⁻⁷ kg/C. Used in batteries and decorative plating.
  • Gold (Au³⁺ + 3e⁻ → Au): Z = 6.81 × 10⁻⁷ kg/C. Decorative and electronics plating.
  • Iron (Fe²⁺ + 2e⁻ → Fe): Z = 2.89 × 10⁻⁷ kg/C.
  • Zinc (Zn²⁺ + 2e⁻ → Zn): Z = 3.39 × 10⁻⁷ kg/C. Industrial electrowinning at 88-94% efficiency.
  • Hydrogen (2H⁺ + 2e⁻ → H₂): Z = 1.045 × 10⁻⁸ kg/C. The lightest plating species; key for clean-energy hydrogen production.
  • Sodium (Na⁺ + e⁻ → Na): Z = 2.38 × 10⁻⁷ kg/C. Down's cell (molten NaCl) for industrial Na production.
  • Aluminum (Al³⁺ + 3e⁻ → Al): Z = 9.32 × 10⁻⁸ kg/C. Hall-Héroult process; ~15 kWh/kg energy intensity.

Worked Example — Nickel Plating

Plate nickel onto a steel substrate at 5 A for 30 min:

  • Q = I × t = 5 A × 1800 s = 9000 C.
  • m = Z × Q = 3.04 × 10⁻⁷ × 9000 = 2.74 × 10⁻³ kg = 2.74 g of Ni.
  • Moles = Q / (n·F) = 9000 / (2 × 96485) = 0.0466 mol.
  • At 95% current efficiency (typical for Watt's bath): actual mass = 2.74 × 0.95 = 2.60 g.
  • If plating onto 100 cm² substrate at uniform thickness: with Ni density 8.9 g/cm³, thickness = 2.60 / (100 × 8.9) = 2.92 × 10⁻³ cm = 29.2 µm nickel coating.

Why Real Cells Are Less Efficient

Faraday's law gives the THEORETICAL maximum at 100% current efficiency. Real cells lose efficiency to side reactions:

  • Hydrogen evolution at the cathode: for less-noble metals (Zn, Fe, Ni, Cr), some current goes to 2H⁺ + 2e⁻ → H₂ instead of metal deposition. This is the dominant inefficiency in chrome plating (10-25% Faradaic efficiency).
  • Oxygen evolution at the anode: the inverse problem at the anode in many electrowinning cells; can also reoxidize freshly-deposited metal at the cathode if the cell isn't designed properly.
  • Re-dissolution of deposited metal: in stop-start operation or with poor anode-cathode separation, freshly-plated metal can dissolve back into solution.
  • Side products from impurities: trace ions (Pb, Sb, As) in copper electrolyte cause rough deposits and lower efficiency.

Typical industrial current efficiencies: Cu electrowinning 85-92%; Zn electrowinning 88-94%; Ni in Watt's bath 95-99%; chromium 10-25%; aluminum (Hall-Héroult) 92-96%; chlor-alkali 96-98%. Always multiply theoretical mass by your empirical current efficiency.

Voltage and Energy in Real Cells

The theoretical minimum voltage is given by the standard cell potential (E0) for the overall reaction. Real cells need substantially more:

  • Standard E0: the thermodynamic minimum (e.g. 1.23 V for water electrolysis at 25 °C, 1.7 V for Hall-Héroult Al).
  • Cathode overpotential η_c: kinetic activation energy at the cathode (typically 50-300 mV for active metals, much higher for H₂ on inert electrodes).
  • Anode overpotential η_a: usually larger than cathode (300-600 mV typical for O₂ evolution).
  • IR drop: ohmic loss in electrolyte, contacts, busbar — often 50-80% of total cell voltage in industrial cells with low-conductivity electrolytes.
  • Concentration polarization: additional loss at high current density when ion supply to electrode surface is mass-transport limited.

Practical voltages: Cu electrowinning ~2 V (vs E0 = 0.34 V); Hall-Héroult Al ~4-5 V (vs E0 = 1.7 V); water electrolysis 1.7-2.0 V (vs E0 = 1.23 V); chlor-alkali ~3-4 V (vs E0 = 2.2 V).

Real-World Example

Electrolysis – Worked Examples

Example 1 — Silver Coulometer (Historical Charge Standard). Pass 1.000 A through a silver coulometer for exactly 1.000 hour.
  • Q = 1 A × 3600 s = 3600 C = 1.000 Ah.
  • m = Z × Q = 1.118×10⁻⁶ × 3600 = 4.025×10⁻³ kg = 4.025 g of silver.
  • Until 1948, the silver coulometer was the official BIPM definition of charge: 1 coulomb = exactly 0.001118 g of Ag deposited.
  • Modern SI defines the coulomb based on the elementary charge (1 C = 6.241 × 10¹⁸ e), but the silver-coulometer measurement is still accurate to ~1 ppm.

Example 2 — Copper Electrowinning Cell. A commercial Cu cell operates at 30,000 A for 24 hours.

  • Q = 30,000 × 86,400 = 2.592×10⁹ C = 720,000 Ah.
  • Theoretical m = 3.294×10⁻⁷ × 2.592×10⁹ = 854 kg of Cu/day.
  • At 90% current efficiency: actual = 769 kg/day = ~280 tonnes/year per cell.
  • At 2 V cell voltage: power = 30,000 × 2 = 60 kW; energy = 60 kW × 24 hr = 1,440 kWh/day.
  • Energy intensity: 1440 / 769 = 1.87 kWh/kg Cu — modern Cu electrowinning is impressively efficient (vs ~15 kWh/kg for Al).

Example 3 — Hydrogen Production Electrolyzer. 50 MW PEM electrolyzer operating at 1.8 V cell voltage, producing H₂ at 75% Faradaic efficiency.

  • Total cell current = 50×10⁶ / 1.8 = 27.8×10⁶ A across all cells in series.
  • Per second: Q = 27.8×10⁶ × 1 = 27.8 MC.
  • Theoretical H₂: m = 1.045×10⁻⁸ × 27.8×10⁶ = 0.290 kg/s.
  • At 75% efficiency: actual H₂ = 0.218 kg/s = 18.8 tonnes/day = ~6,860 tonnes/year.
  • Energy intensity: 50,000 kW / (0.218 × 3600) = 63.7 kWh/kg H₂ — typical for PEM (lower for alkaline at ~50 kWh/kg, much lower for theoretical 33 kWh/kg minimum).

Example 4 — Decorative Gold Electroplating. Gold-plate a watch case at 0.5 A for 10 minutes from a citrate-cyanide bath.

  • Q = 0.5 × 600 = 300 C.
  • Theoretical m = 6.81×10⁻⁷ × 300 = 2.04×10⁻⁴ kg = 0.204 g = 204 mg of gold.
  • At 99% current efficiency (typical Au baths): actual = 202 mg.
  • If watch case has 30 cm² plated area at uniform thickness, with Au density 19.3 g/cm³: thickness = 0.202 / (30 × 19.3) = 3.5×10⁻⁴ cm = 3.5 µm gold layer.
  • Cost at $80/g pure gold: ~$16 of gold consumed (much more in commercial bath operation due to drag-out, side reactions, and bath maintenance).

Example 5 — Hall-Héroult Aluminum Cell. Industrial cell operating at 350 kA for 24 hours.

  • Q = 350,000 × 86,400 = 3.024×10¹⁰ C.
  • Theoretical Al: m = 9.32×10⁻⁸ × 3.024×10¹⁰ = 2,818 kg = 2.82 tonnes/day per cell.
  • At 95% current efficiency: actual = 2,677 kg/day = ~977 tonnes/year per cell.
  • Cell voltage 4.5 V; power = 350,000 × 4.5 = 1,575 kW per cell; daily energy = 37,800 kWh.
  • Energy intensity: 37,800 / 2,677 = 14.1 kWh/kg Al — close to modern industry best (13-15 kWh/kg). Theoretical minimum is ~6 kWh/kg, but kinetic and ohmic losses dominate.
  • A typical Al smelter has 200-300 cells in series pulling 700,000+ amps total — among the largest electrical loads in any industry.

Who Should Use the Electrolysis Calculator?

1
Electrochemistry Students: Standard exercise covering Faraday's laws, electrochemical equivalents, and the relationship between current, time, and mass deposited. Foundational for upper-level inorganic and physical chemistry courses.
2
Electroplating Shops: Compute plating bath operating parameters; size DC power supplies for target thickness × area × duration; troubleshoot off-spec deposit masses.
3
Electrowinning / Electrorefining Process Engineers: Plant-scale Cu, Zn, Ni, Mn, Co electrowinning operating point design; current-efficiency tracking and root-cause analysis when below spec.
4
Hydrogen-Economy / Clean-Energy Engineers: Size electrolyzers (alkaline, PEM, SOEC) for green-hydrogen projects; compute capital and operating cost per kg H₂; track Faradaic efficiency vs voltage efficiency.
5
Battery Researchers: Quantify charge-transfer in Li-ion intercalation, deposition / stripping efficiency in metal-anode batteries (Li, Zn, Mg), capacity-fade analysis.
6
Analytical Chemists / Coulometric Methods: Coulometric titration for accurate trace-analyte determination; controlled-potential electrolysis for sample pre-concentration.
7
Aluminum-Smelter Operators: Hall-Héroult cell production targets; current-efficiency monitoring (typical 90-96%); energy-intensity benchmarking against industry best practice (~13-15 kWh/kg Al).

Technical Reference

Historical Context. Michael Faraday published his First and Second Laws of Electrolysis in 1834 (Phil. Trans. Royal Society 124). The First Law: mass deposited is proportional to charge passed. The Second Law: equivalent masses of different elements are deposited by the same charge — m₁/m₂ = E₁/E₂ where E = M/n is the equivalent weight. Together they imply the existence of a universal "electrochemical equivalent" — a precursor concept to the elementary charge (e ≈ 1.602×10⁻¹⁹ C, formally defined in 2019 SI as exact). The Faraday constant F = N_A × e = 96,485.33212... C/mol is one of the most-precisely-known constants in physics.

The Faraday Constant F. F = 96,485.33212 C/mol is the charge of one mole (Avogadro's number, N_A = 6.022×10²³) of electrons. Equivalently, F = 26.8 Ah/mol (= 96,485 / 3,600). Mnemonic check: 1 mole of any singly-charged ion (n = 1) requires F = 96,485 C to deposit; 1 mole of doubly-charged (n = 2) requires 2F = 192,970 C; 1 mole of triply-charged (n = 3) requires 3F = 289,455 C.

Z Values for Common Half-Reactions:

  • Silver (Ag⁺ + e⁻ → Ag, n=1): Z = 107.868 / (1 × 96485) = 1.118×10⁻³ g/C = 1.118 mg/C. The historical "silver coulometer" reference.
  • Copper (Cu²⁺ + 2e⁻ → Cu, n=2): Z = 63.546 / (2 × 96485) = 3.294×10⁻⁴ g/C = 0.3294 mg/C. Industrial standard.
  • Cuprous Cu (Cu⁺ + e⁻ → Cu, n=1): Z = 6.589×10⁻⁴ g/C — used in cuprous-based plating baths (rare).
  • Nickel (Ni²⁺ + 2e⁻ → Ni, n=2): Z = 58.6934 / (2 × 96485) = 3.04×10⁻⁴ g/C.
  • Gold (Au³⁺ + 3e⁻ → Au, n=3): Z = 196.967 / (3 × 96485) = 6.81×10⁻⁴ g/C.
  • Aurous Au (Au⁺ + e⁻ → Au, n=1): Z = 2.04×10⁻³ g/C — common in cyanide gold-plating baths.
  • Iron — ferrous (Fe²⁺ + 2e⁻ → Fe, n=2): Z = 2.89×10⁻⁴ g/C.
  • Iron — ferric (Fe³⁺ + 3e⁻ → Fe, n=3): Z = 1.93×10⁻⁴ g/C.
  • Zinc (Zn²⁺ + 2e⁻ → Zn, n=2): Z = 3.39×10⁻⁴ g/C.
  • Hydrogen (2H⁺ + 2e⁻ → H₂, n=2): Z = 2.016 / (2 × 96485) = 1.045×10⁻⁵ g/C = 10.45 µg/C.
  • Oxygen (2H₂O → O₂ + 4H⁺ + 4e⁻, n=4): Z(O₂) = 31.998 / (4 × 96485) = 8.29×10⁻⁵ g/C — anode product in water electrolysis.
  • Sodium (Na⁺ + e⁻ → Na, n=1): Z = 2.38×10⁻⁴ g/C.
  • Potassium (K⁺ + e⁻ → K, n=1): Z = 4.05×10⁻⁴ g/C.
  • Aluminum (Al³⁺ + 3e⁻ → Al, n=3): Z = 9.32×10⁻⁵ g/C.
  • Magnesium (Mg²⁺ + 2e⁻ → Mg, n=2): Z = 1.26×10⁻⁴ g/C — molten MgCl₂ electrolysis.
  • Lithium (Li⁺ + e⁻ → Li, n=1): Z = 7.19×10⁻⁵ g/C — molten LiCl-KCl electrolysis.
  • Chromium (Cr⁶⁺ + 6e⁻ → Cr, n=6, hexavalent chrome plating): Z = 8.98×10⁻⁵ g/C — but real chrome plating runs at 10-25% Faradaic efficiency, so apparent Z is much lower.

Industrial Current Efficiencies (Empirical):

  • Copper electrowinning (CuSO₄ acid bath): 85-92%. Losses to H₂ co-evolution (~5%), impurity reduction (~3%), and short-circuiting cathode-to-anode contact in operational cells.
  • Copper electrorefining (anode → cathode purification): 95-99%. Higher than electrowinning because anode dissolves at near-100% efficiency too.
  • Zinc electrowinning (acid sulfate): 88-94%. Hydrogen evolution is the dominant loss; bath additives (gum arabic, glue) suppress H₂.
  • Nickel plating (Watt's bath, sulfate-chloride): 95-99%. Among the most-efficient industrial plating processes.
  • Chromium plating (chromic acid + sulfate catalyst): 10-25%. Most current goes to H₂ evolution; the inefficiency is intrinsic to hexavalent-chrome chemistry. Trivalent-chrome plating (developed since 1990s) achieves 50-70% efficiency.
  • Aluminum (Hall-Héroult): 92-96%. Losses to back-reaction at cathode (Al + 3CO₂ → Al₂O₃ + 3CO) and side-reactions with cell carbon.
  • Hydrogen production — alkaline electrolyzer: 70-80% Faradaic; voltage efficiency 60-70%; round-trip energy efficiency 50-65%.
  • Hydrogen production — PEM electrolyzer: 80-90% Faradaic; voltage efficiency 70-80%; total round-trip 65-75%.
  • Hydrogen production — SOEC (high-temp solid-oxide): 90-95% Faradaic; voltage efficiency 85-95%; total 80-90% — highest efficiency but operating challenges.
  • Chlor-alkali (membrane cell): 96-98%. Modern membrane cells are essentially the cleanest large-scale electrolysis.

Voltage Components in Industrial Cells:

  • Standard cell potential E0 (thermodynamic minimum): e.g. 1.23 V for water, 1.7 V for Hall-Héroult, 0.34 V for Cu²⁺/Cu, 2.21 V for chlor-alkali.
  • Overpotentials η_a + η_c (kinetic activation): 100-600 mV total for active electrode-electrolyte combinations; up to 1+ V for slow kinetics or inert electrodes.
  • IR drop (ohmic resistance): often 0.5-2 V in industrial cells with low-conductivity electrolytes (e.g. molten cryolite for Al). Reduces with electrolyte conductivity, electrode separation, and operating current density.
  • Concentration polarization (mass-transport limit): at high current density, ion supply to electrode surface becomes rate-limiting; manifests as additional voltage drop at >50-70% of limiting current density.

Practical industrial cell voltages: Cu electrowinning ~2.0 V (vs E0 = 0.34 V); Zn electrowinning ~3.3 V (vs E0 = -0.76 V, but standard cell potential is the difference H₂O/O₂ at anode minus Zn at cathode = ~2 V); Al Hall-Héroult ~4-5 V (vs E0 ~1.7 V); water electrolysis (alkaline) 1.85-2.05 V (vs E0 = 1.23 V); chlor-alkali ~3.0-3.8 V (vs E0 = 2.21 V).

Energy Intensity Benchmarks:

  • Aluminum (Hall-Héroult): 13-15 kWh/kg (industry best 12.5; theoretical minimum 6.0). The single largest electrical load per unit mass of any commodity metal.
  • Copper electrowinning: 1.7-2.5 kWh/kg.
  • Zinc electrowinning: 3.0-3.5 kWh/kg.
  • Nickel electrowinning: 3.5-4.5 kWh/kg.
  • Chrome plating: 5-15 kWh/kg of Cr deposited (poor due to low Faradaic efficiency).
  • Hydrogen — alkaline electrolyzer: 50-55 kWh/kg H₂ (theoretical minimum 33 kWh/kg).
  • Hydrogen — PEM electrolyzer: 53-60 kWh/kg.
  • Hydrogen — SOEC: 35-45 kWh/kg (closest to theoretical).
  • Chlor-alkali: 2,500-2,900 kWh/tonne Cl₂ (modern membrane cells).

Key Takeaways

Faraday's First Law of Electrolysis is the cornerstone equation of electrochemistry: m = Z × Q = Z × I × t — mass deposited equals the electrochemical equivalent times the total charge passed. The electrochemical equivalent Z = M / (n × F) where M is molar mass, n is valency, and F = 96,485 C/mol. Reference Z values for common species: Ag 1.118 µg/C, Cu 0.329 µg/C, Ni 0.304 µg/C, Au 0.681 µg/C, Fe 0.289 µg/C, Zn 0.339 µg/C, H₂ 10.45 ng/C, Al 0.0932 µg/C. Critical caveat: Faraday's law gives THEORETICAL mass at 100% current efficiency. Real cells: Cu electrowinning 85-92%, Zn 88-94%, Ni 95-99%, chrome plating 10-25%, Al Hall-Héroult 92-96%, chlor-alkali 96-98%. Multiply theoretical mass by empirical current efficiency for realistic estimates. Voltage requirements: industrial cells run at 2-5× the standard E0 due to overpotentials, IR drop, and concentration polarization — Cu electrowinning ~2 V (vs E0 = 0.34 V); Hall-Héroult Al ~4-5 V (vs E0 = 1.7 V); water electrolysis 1.7-2.0 V (vs E0 = 1.23 V).

Frequently Asked Questions

What is the Electrolysis Calculator?
It implements Faraday's First Law of Electrolysis (1834): m = Z × Q = Z × I × t, where m is the mass deposited at the electrode, Z = M/(n·F) is the electrochemical equivalent (kg/C), Q is the total charge passed (C), I is the current (A), and t is the time (s). The calculator auto-fills Z for 12 common species (Ag, Cu, Ni, Au, Fe, Zn, H₂, Na, K, O₂, Al) plus a Custom mode. Output: theoretical mass deposited, charge in C and Ah, moles deposited, and energy estimate at standard cell potential.

Designed for electrochemistry students, electroplating shops, electrowinning process engineers, hydrogen-economy / clean-energy engineers, and analytical-chemistry coulometric workflows.

Pro Tip: Pair this with our Serial Dilution Calculator for analytical-chemistry standard preparation.

What is Faraday's First Law of Electrolysis?
Published by Michael Faraday in 1834: the mass of substance deposited at an electrode is directly proportional to the total electric charge passed through the cell. Mathematically: m = Z × Q where Z is the proportionality constant called the electrochemical equivalent. Combined with Faraday's Second Law (equivalent masses are proportional to atomic mass / valency), this implies the universal Faraday constant F = 96,485 C/mol — the charge of one mole of electrons. Together, the laws are the foundation of all quantitative electrochemistry.
What is the electrochemical equivalent Z?
Z = M / (n × F), where M is the molar mass (kg/mol — divide g/mol values by 1000), n is the valency (electrons transferred per ion), and F = 96,485 C/mol is the Faraday constant. Z gives the mass of element deposited per coulomb of charge. Common values: Silver (Ag⁺) Z = 1.118 mg/C; Copper (Cu²⁺) Z = 0.329 mg/C; Nickel (Ni²⁺) Z = 0.304 mg/C (matches the screenshot example of 3.04×10⁻⁷ kg/C); Hydrogen (H₂) Z = 10.45 µg/C; Aluminum (Al³⁺) Z = 0.0932 mg/C. Z is reaction-specific — for unusual oxidation states (e.g. Cu⁺ instead of Cu²⁺), use the appropriate n.
How is the calculator's mass output the THEORETICAL maximum?
Faraday's law assumes 100% Faradaic efficiency — every electron passed through the cell deposits exactly one ion's worth of metal at the cathode. Real cells have side reactions that consume some current without depositing the target metal: hydrogen co-evolution (2H⁺ + 2e⁻ → H₂) at the cathode, oxygen evolution at the anode, re-dissolution of freshly-plated metal, reduction of impurity ions. Typical industrial Faradaic efficiencies: Cu electrowinning 85-92%; Zn 88-94%; Ni 95-99%; chrome plating 10-25%; Al (Hall-Héroult) 92-96%; chlor-alkali 96-98%. Multiply theoretical mass by your empirical current efficiency for realistic estimates.
What's the Faraday constant?
F = 96,485.33212 C/mol — the electric charge of one mole (6.022×10²³) of electrons. Or equivalently F = 26.8 Ah/mol. Mnemonic: 1 mole of any singly-charged ion (n=1) requires exactly F coulombs to deposit; 1 mole of doubly-charged ion (n=2) requires 2F = 192,970 C; 1 mole of triply-charged ion (n=3) requires 3F = 289,455 C. F is one of the most-precisely-known constants in physics, defined exactly in the 2019 SI redefinition based on the elementary charge e and Avogadro's number N_A.
Why is real cell voltage higher than the standard E0?
Industrial cells run at 2-5× the thermodynamic minimum E0 due to four overpotential / loss mechanisms: (1) Cathode overpotential η_c — kinetic activation energy at the cathode (50-300 mV typical). (2) Anode overpotential η_a — usually larger than cathode (300-600 mV typical, especially for O₂ evolution). (3) IR drop — ohmic resistance in electrolyte / contacts / busbar (often 50-80% of total cell voltage in industrial cells with low-conductivity electrolytes). (4) Concentration polarization — additional voltage at high current density when ion supply to the electrode surface is mass-transport-limited. Practical voltages: Cu electrowinning ~2 V (vs E0 = 0.34 V); Hall-Héroult Al ~4-5 V (vs E0 = 1.7 V); water electrolysis 1.7-2.0 V (vs E0 = 1.23 V).
How much energy does industrial-scale electrolysis use?
Energy intensities (kWh per kg of product, modern industry best practice): Aluminum (Hall-Héroult): 13-15 kWh/kg — the most energy-intensive commodity metal; theoretical minimum ~6 kWh/kg. Copper electrowinning: 1.7-2.5 kWh/kg. Zinc: 3.0-3.5 kWh/kg. Nickel: 3.5-4.5 kWh/kg. Hydrogen — alkaline electrolyzer: 50-55 kWh/kg H₂ (theoretical 33). Hydrogen — PEM: 53-60 kWh/kg. Hydrogen — SOEC: 35-45 kWh/kg. Chlor-alkali: 2,500-2,900 kWh/tonne Cl₂. Aluminum smelters and chlor-alkali plants are typically the largest electrical loads in any industrial complex.
Why is chrome plating so inefficient?
Hexavalent-chrome plating (the standard industrial process using chromic acid + sulfate catalyst) operates at only 10-25% Faradaic efficiency — most of the current goes to hydrogen evolution at the cathode (2H⁺ + 2e⁻ → H₂) instead of chromium reduction. The inefficiency is intrinsic to hexavalent-chrome chemistry: Cr⁶⁺ + 6e⁻ → Cr is a 6-electron process with very slow kinetics, while H⁺ + e⁻ → ½H₂ has fast kinetics. Modern trivalent-chrome plating (developed since the 1990s for environmental reasons — Cr⁶⁺ is carcinogenic) achieves 50-70% efficiency with Cr³⁺ + 3e⁻ → Cr. This is why chrome plating is so expensive per kg of Cr deposited (5-15 kWh/kg vs Cu's 2 kWh/kg).
Can I use the calculator for batteries?
Yes, with caveats. Faraday's law applies to any electrochemical cell — battery discharge/charge is just controlled-potential electrolysis. For Li-ion: 1 Ah of charge = 1 × 3600 / 96485 = 0.0373 mol of Li transferred. With Li atomic mass 6.94 g/mol: 0.0373 × 6.94 = 0.259 g Li per Ah. However: battery capacity is normally expressed in Ah at a specific voltage, not absolute charge — the calculator gives Faradaic charge but doesn't compute battery-specific capacity (mAh/g of active material) or coulombic efficiency (a battery-specific term related to but distinct from Faradaic efficiency). For battery-cell design, use specialized battery-cell calculators that account for active-material loading, voltage curves, and intercalation chemistry.
What does 'Custom' element mode do?
Custom mode lets you enter the electrochemical equivalent Z directly in kg/C, useful for: (1) unusual oxidation states not covered by the 12 preset elements (e.g. Cu⁺ instead of Cu²⁺ for cuprous baths); (2) compound electrolysis where the deposited species is a compound, not an element (e.g. PbO₂ deposition for batteries, MnO₂ for batteries); (3) species not in the preset list (Mg, Li, Co, Mn, etc.). Compute Z = M / (n × F) using your specific reaction's molar mass and electron count, then enter the value. Custom mode disables the energy estimate (which requires a known E0 standard reduction potential).
How do I check the calculator's output is right?
Two sanity checks: (1) 1 amp for 1 hour at the standard silver-coulometer reaction should give exactly 4.025 g of silver (the historical definition before the 2019 SI redefinition). Test: pick Silver, enter I = 1 A, t = 1 hr → calculator should output m = 4.025 g, Q = 3,600 C = 1.000 Ah. (2) Hand-check the Faraday formula: For Nickel (M = 58.69, n = 2), 5 amps for 30 minutes: Q = 5 × 1800 = 9000 C; mol = 9000 / (2 × 96485) = 0.0466; mass = 0.0466 × 58.69 = 2.74 g. Calculator should match within ~0.5% rounding.

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The ToolsACE Team - ToolsACE.io Team

The ToolsACE Team

Our ToolsACE electrochemistry team built this calculator on Michael Faraday's First Law of Electrolysis (1834): the mass of substance deposited at an electrode is directly proportional to the total electric charge passed through the cell. <strong>m = Z × Q = Z × I × t</strong>, where Z is the electrochemical equivalent (M / (n·F) — molar mass divided by valency × Faraday constant). The calculator auto-fills Z for 12 common electroplating and electrowinning species: Silver (Z = 1.118 µg/C, the historical 'silver coulometer' standard), Copper (3.29 µg/C, the most-used industrial electroplating species), Nickel, Gold, Iron, Zinc, Hydrogen, Sodium, Potassium, Oxygen, Aluminum, and Custom for any species not in the list. Inputs accept current in A / mA / kA, time in s / min / hr / days, and the calculator outputs mass deposited in g / kg / mg, total charge passed in C / kC / Ah, theoretical voltage required (assuming standard cell potentials), and approximate energy consumption — useful for sizing electroplating baths, electrowinning cells, and electrochemistry teaching demonstrations.

Faraday's First Law of Electrolysis (1834)IUPAC Atomic MassesCRC Handbook of Chemistry and Physics

Disclaimer

Faraday's law gives the THEORETICAL maximum mass deposited at 100% current efficiency. Real electrolysis cells operate at 60-99% current efficiency depending on species, electrolyte, current density, temperature, and side reactions (notably hydrogen evolution at the cathode for less-noble metals like Zn, Fe, Ni, and oxygen evolution at the anode). For copper electrowinning, expect 85-92% efficiency; zinc 88-94%; nickel 95-99%; chrome plating 10-25%; aluminum (Hall-Héroult) 92-96%. Multiply theoretical mass by empirical current efficiency. The calculator does not account for IR drop, overpotentials, concentration polarization, electrode area effects, or surface roughness on plating quality. For industrial cell design, consult a process engineer and verify with empirical bench-scale tests. Source data: Faraday (1834) Phil. Trans. Royal Society 124, IUPAC atomic masses, CRC Handbook of Chemistry and Physics, standard electrochemistry textbooks (Bard & Faulkner, Newman & Thomas-Alyea).