Electroplating Thickness Calculations (Faraday's Law Made Simple) | Lab Wizard
Table of Contents
Electroplating Thickness Calculations (Faraday’s Law Made Simple)
Electroplating thickness is one of the most critical measurements in metal finishing, affecting cost, material performance, solderability, corrosion resistance, and audit compliance.
But most shops still calculate plating thickness manually using spreadsheets, tribal knowledge, or “rules of thumb” that aren’t always accurate.
This guide explains exactly how to calculate thickness using Faraday’s Law, what assumptions matter, and how to avoid common mistakes that cause scrap, rework, or failed customer audits.
⚡ Quick Summary: What Faraday’s Law Says
Faraday’s Law connects electrical charge to mass deposited during electroplating:
More current × more time = more metal deposited.
The material, valence, and current efficiency determine how much.
🧮 The Core Formula: Faraday’s Law for Plating Thickness
Let’s start with the full version used in plating engineering:
Thickness (inches) = (I × T × C.E. × EW) / (d × A × F × V × 231)
Where:
| Symbol | Meaning |
|---|---|
| I | Current (amperes) |
| T | Time (seconds) |
| C.E. | Current efficiency (decimal) |
| EW | Equivalent weight = atomic weight / valence |
| d | Density of metal (g/cm³) |
| A | Surface area (in²) |
| F | Faraday constant (96,485 coulombs) |
| 231 | Conversion factor (cubic inches → mL/in³ etc.) |
| V | Valence of the metal ion |
But plating shops rarely use the long formula directly.
Instead, Faraday’s Law simplifies into very useful “rules of thumb.”
⚙️ Simplified Thickness Formula (Used in Most Shops)
For practical production:
Thickness (microinches) = k × (Amp-Hours) / Area (ft²)
Where k is a metal specific constant.
Common “k” Factors (Approximate)
| Metal | Typical k-Factor (µin per amp-hour per ft²) |
|---|---|
| Nickel | 267–300 µin/ASFH |
| Copper | 550–600 µin/ASFH |
| Chrome (hard) | 110–130 µin/ASFH |
| Tin | 900–1000 µin/ASFH |
| Gold | 1200–1400 µin/ASFH |
These factors already include valence, density effects, Faraday constant, and efficiency assumptions.
🔧 Step By Step Thickness Calculation (Example)
Goal: Plate 0.0003" (300 microinches) of Nickel
Panel area: 1.2 ft²
Bath efficiency: 95% (0.95)
k-factor for nickel: 280 µin/AH/ft²
1️⃣ Calculate amp-hours required
Since k-factors are typically theoretical values, apply current efficiency explicitly:
Required AH = (Thickness × Area) / (k × C.E.)
= (300 µin × 1.2 ft²) / (280 × 0.95)
= 360 / 266
= 1.35 AH
2️⃣ Choose current and calculate time
If you run at 30 amps:
Time (hrs) = AH / Amps
= 1.35 / 30
= 0.045 hrs
Convert to minutes:
0.045 × 60 = 2.7 minutes
✔️ At 30 A, you will reach 300 µin in about 2.7 minutes.
📘 Faraday Based Formula for Exact Precision
If auditors demand traceability or if you’re plating aerospace/defense parts, use the scientific formula:
Thickness = (I × T × C.E. × EW) / (d × A × 96,485)
Example values:
- Nickel atomic weight: 58.69
- Valence: 2
- EW: 29.35
- Density: 8.9 g/cm³
- C.E.: 0.9–1.0
🧪 Nickel Thickness Lookup Table (Quick Reference)
| ASF | Minutes | Approx Nickel Thickness (µin) |
|---|---|---|
| 10 | 10 | 60–70 |
| 20 | 10 | 120–140 |
| 30 | 10 | 180–210 |
| 30 | 5 | 90–105 |
| 40 | 10 | 240–280 |
(Your chemistry supplier’s TDS may differ, always verify.)
💡 Note on Throwing Power
Thickness calculations based on Faraday’s Law assume uniform current distribution. In practice, throwing power and part geometry influence where metal actually deposits. Even with correct amp-hour calculations, low throwing power can produce thin deposits in recesses or shadowed areas.
For distribution focused analysis, see our Hull Cell Tips & Tricks guide.
🚩 Critical Mistakes Most Shops Make
❌ Mistake #1 — Assuming 100% current efficiency
Nickel sulfamate is ~95–100%.
Gold cyanide can be 90%.
Chrome plating can be less than 20%.
This drastically changes thickness.
❌ Mistake #2 — Using incorrect surface area
Undercalculated area → thickness too thin
Overcalculated → thickness too thick
Multi-surface parts need separate area estimates.
❌ Mistake #3 — Using amps instead of amp-hours
Thickness depends on total charge, not current alone.
❌ Mistake #4 — Forgetting to convert units
in² vs ft²
mils vs microns
±10% errors instantly appear.
❌ Mistake #5 — Not monitoring rectifier drift
Even a small drop in current causes thickness variation.
Lab Wizard’s rectifier monitoring tracks:
- amperage
- voltage
- drift
- waveform bursts
Contact us for more information about rectifier monitoring solutions.
🧰 Tools to Improve Thickness Accuracy
✔ Hull Cell Tests
Diagnostics for throwing power and deposit distribution.
✔ Amp-Minute / Amp-Hour Tracking
Use meters that record cumulative charge delivered. Lab Wizard offers automated rectifier monitoring solutions that track amp-hours in real time. Contact us for more information.
✔ Rectifier Waveform Monitoring
Detects ripple, imbalance, and current starvation. Lab Wizard offers automated rectifier monitoring solutions that integrate directly with Lab Wizard Cloud. Contact us for more information.
📦 Final Thought
Faraday’s Law isn’t complicated once you break it down.
If you know:
- Current
- Time
- Area
- Efficiency
…you can predict thickness reliably.
Related resources
- How to Calculate Chemical Additions & Rebuild Plating Baths
- Hull Cell Tips & Tricks for Electroplating
- SPC in Plating 101
- How to Set Control Limits in Plating Shops
External references
- U.S. EPA – Pollution Prevention in Metal Finishing (Drag-Out Reduction)
- NASF – Rinse Water Management & Drag-Out Control Guidance
- ASM Handbook Volume 5: Surface Engineering
- NIST Engineering Statistics Handbook – Process Monitoring Concepts
- ASTM B322 – Standard Guide for Cleaning Metals Prior to Electroplating
Master Faraday’s Law now, and thickness variation becomes predictable, not mysterious.