Calculate metal deposition mass, film thickness, and power consumption from current, time, and electrode area using Faraday's laws in real time. Supports Cu, Ni, Cr, Zn, Au, Ag plating and water electrolysis.
Input Parameters
A
min
cm²
Results
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Deposition Mass m (mg)
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Coating Thickness δ (μm)
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Electric Charge Q (C)
—
Energy Use (Wh)
Faraday's Law
$m = \dfrac{\eta M I t}{n F}, \quad F = 96485$ C/mol
Film thickness: $\delta = \dfrac{m}{\rho \cdot A_c}\times 10^3\;\mathrm{[\mu m]}$
Water electrolysis: $V_{H_2} = \dfrac{\eta I t}{2F} \times 22400$ mL
What is the Electrolysis & Electroplating Calculator?
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In electroplating, does metal just stick to the surface when you pass current through it? It feels like magic, and I don't understand the principle at all...
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Roughly speaking, here's how it works. Copper is dissolved in the plating solution to form Cu²⁺ ions, and then current is applied. Electrons are supplied to the cathode (the part you want to plate), so the Cu²⁺ in the solution receives those electrons and deposits as metallic copper on the surface via the reaction 'Cu²⁺ + 2e⁻ → Cu'. Two electrons for one copper atom—that's the core of Faraday's law. Try moving the current slider in the tool. You can see that the higher the current, the more the deposition amount increases.
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The parameter 'current efficiency η' is set to 0.90. What does this ratio represent?
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It's the proportion of the applied current that actually goes into metal deposition. The remaining 10% is mainly consumed by the hydrogen gas evolution reaction '2H⁺ + 2e⁻ → H₂↑'. Chrome plating is particularly bad, with current efficiency only around 10–20%—the remaining 80–90% just wastes current producing hydrogen. If you look at the 'Material Comparison' tab, you can see at a glance the standard current efficiencies for each material (Cr is extremely low) and the corresponding variation in deposition amount and film thickness.
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I see. In the 'Film Thickness vs. Current Density' tab, the film thickness increases linearly with current density. In practice, can you just keep increasing the current to make it as thick as you want?
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Theoretically yes, but in reality there are limits. If the current density is too high, a phenomenon called 'burning' occurs—the deposited metal becomes dark or powdery, and adhesion becomes terrible. Also, when a lot of hydrogen bubbles form, they can attach to the surface, causing the plating to peel off or creating pinholes. Each metal has a 'usable current density range'; for copper plating, 1–5 A/dm² is typical. Try adjusting the 'cathode area' and 'current' in the tool to calculate the current density and check the appropriate range.
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When plating complex-shaped parts in a factory, what makes it difficult?
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The biggest challenge is 'non-uniform current distribution'. Protruding parts concentrate current lines, so the plating becomes thicker, while deep recesses receive less current, making the plating thinner. For example, when you want to apply uniform nickel plating to a smartphone metal frame, the inner curved surfaces might receive only one-fifth of the current that the outer surfaces get. To solve this, 'auxiliary anodes' are placed in tight spots, or 'shields' block current on protruding areas. This tool assumes a uniform distribution, so consider it as a design value for the average film thickness.
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When I switch to 'Water Electrolysis', 'H₂ mass' is displayed. Is this related to 'green hydrogen' production?
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Exactly! Water electrolysis follows the reaction 'H₂O → H₂ + ½O₂', producing hydrogen at the cathode and oxygen at the anode. If you use electricity generated from renewable energy (solar, wind), you can produce green hydrogen with zero CO₂ emissions. By changing the current and time in the tool, you can calculate how many grams of hydrogen are produced. From Faraday's law, 2F of electric charge produces 1 mol of H₂ (2 g). Producing 1 kg of hydrogen requires about 53 kWh of electricity—this is a current industrial benchmark, so please compare it with the tool's numbers.
Physical Model & Key Equations
Combined form of Faraday's first and second laws of electrolysis. Metal deposition is proportional to electric charge \(Q = It\).
$$m = \frac{\eta M I t}{n F}, \quad F = 96485 \text{ C/mol}$$
m: deposited metal mass [g], η: current efficiency, M: molar mass [g/mol], I: current [A], t: time [s], n: metal-ion valence, F: Faraday constant (96485 C/mol).
Conversion from deposited metal mass to coating thickness.
For water electrolysis, the hydrogen volume generated at the cathode under standard conditions is:
$$V_{H_2}\,[\text{mL}] = \frac{\eta I t}{2F} \times 22400$$
How to Use the Three Tabs
Deposition vs Time: Compares deposition over time for three currents centered on the current setting: I/2, I, and 2I. Each trace is linear, and its slope is proportional to current. The slope differs strongly by material; for example, silver deposits faster than gold because its M/n value is higher.
Thickness vs Current Density: Shows how coating thickness, or H₂ generation in water electrolysis mode, changes as current density (mA/cm²) changes. The yellow point marks the current setting. Thickness increases linearly with current density, but quality deteriorates in practice if the proper range is exceeded (for example, about 10-50 mA/cm² for Cu).
Material Comparison: Compares standard current efficiency, deposition mass, and coating thickness for each metal under the current settings for current and time. It makes chromium's very low current efficiency visible, and also shows that gold and silver can produce thinner coatings because their densities are high even when deposited mass is small.
Frequently Asked Questions
What is Faraday's law?
Faraday's law states that the amount of substance deposited during electrolysis is exactly proportional to the electric charge passed (current × time). The formula is m = ηMIt/(nF). When 1 mole of electrons (Faraday constant F = 96485 C) flows, 1/n moles of n-valent metal ions are deposited. For example, for Cu²⁺ (n=2), two electrons are consumed to deposit one copper atom.
Why are metals with low current efficiency η (e.g., chromium) still used?
Chromium has an extremely low current efficiency of 10–20%, but its very hard coating (Vickers hardness 800–1000 HV) and excellent corrosion and wear resistance make it indispensable for industrial parts and decorative applications. The low efficiency results in higher power consumption and greater burden on the electrolyte, and environmental regulations (RoHS, REACH) for hexavalent chromium must be addressed. In recent years, there has been a shift toward trivalent chromium plating.
How is plating thickness calculated? Is it uniform?
Thickness is calculated as δ = m / (ρ × A_c) × 10³ [μm]. This gives the average thickness assuming uniform deposition over the entire area A_c. In practice, complex shapes cause non-uniform current distribution, leading to thicker deposits on protrusions and thinner deposits in recesses (throwing power issue). To achieve uniform thickness, auxiliary anodes, shields, and optimized agitation are necessary.
What happens if the current density is too high?
When the current density exceeds the upper limit, 'burned deposit' occurs, resulting in dark or powdery coatings. Hydrogen bubble generation also increases, and bubbles adhering to the surface can cause pinholes and peeling. Designing within the appropriate current density range for each metal (e.g., copper 1–5 A/dm², nickel 1–10 A/dm²) is fundamental for quality assurance.
What is the calculation guideline for green hydrogen production via water electrolysis?
Theoretically, 2F = 2 × 96485 = 192970 C (about 53.6 Ah) produces 1 mol (2 g) of hydrogen. To produce 1 kg of hydrogen, about 26.8 kWh is theoretically required, but actual electrolyzers consume about 50–60 kWh/kg due to overpotential and heat losses. By setting current and time in this tool, you can estimate hydrogen production for a specific system.
How should power consumption be calculated?
Power consumption [Wh] is roughly calculated as bath voltage V_bath × current I × time [h]. This tool provides a simplified calculation without assuming bath voltage, but actual electrolyzer voltage varies from 3 to 10 V depending on electrolyte type, temperature, and electrode gap. For copper plating, about 3–5 V is typical; for chromium plating, 6–10 V. Accurate energy calculation requires monitoring the actual bath voltage.
What is Electrolysis?
Electrolysis is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind Electrolysis Calculator (Faraday's Law). Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind Electrolysis Calculator (Faraday's Law) are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.
Enter current in amperes (A) using the I slider or input field—typical electroplating processes use 5–50 A
Set time in seconds (s) via the T slider; industrial copper electrorefining runs 8–24 hours (28,800–86,400 s)
Input atomic mass in g/mol and valence (charge state) for your target metal—copper is 63.5 g/mol with valence +2
The calculator applies Faraday's second law: mass = (I × t × M)/(n × F), where F = 96,485 C/mol
Worked Example
Electroplate mild steel with nickel at 20 A for 3,600 s (1 hour). Nickel: M = 58.7 g/mol, valence n = +2. Mass deposited = (20 × 3,600 × 58.7)/(2 × 96,485) = 7.28 g. For a 0.1 m² cathode, thickness = 7.28 g ÷ (8,900 kg/m³ density) ÷ 0.1 m² = 0.82 mm coating.
Practical Notes
Current efficiency rarely reaches 100%—aluminum smelting operates at 85–95% due to side reactions; reduce calculated mass by your process efficiency factor
Temperature affects conductivity; use higher current density (A/dm²) at 50–60 °C for chromium plating to prevent hydrogen embrittlement
Valence state varies by ion: Fe²⁺ has n=2, Fe³⁺ has n=3; verify from your electrolyte chemistry before calculation