Why Calculated and Measured Plating Thickness Differ
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Why Calculated and Measured Plating Thickness Differ
Calculated plating thickness and measured coating thickness answer different questions. Faraday’s law estimates the mass of metal a defined cathode reaction can deposit from electrical charge and current efficiency. A single thickness number appears only after you add a deposit density and a surface area, and that number is an average over the area you declared. The thickness at an edge, on a flat, or in a recess depends on where the current went.
The ampere-hours can be on the rectifier log, and the area can be on the traveler, while a recess still reads thin. Those numbers aren’t necessarily in conflict. The calculation may describe the average deposit while the gauge measures one location.
A disagreement cannot be interpreted until you know whether the two numbers represent the same quantity, the same area, and the same location.
Electroplating Thickness Calculations (Faraday’s Law Made Simple) is the worksheet for the arithmetic. This article is about what to compare when that worksheet and the part disagree.
🎯 What the Charge Equation Returns
For electrodeposition of one metal by a known half-reaction, the deposited mass is
m = (I × t × M × η) / (n × F)
m is mass, I is current, t is time, M is the molar mass of the deposited metal, η is the cathode current efficiency as a fraction, n is the number of electrons in the half-reaction, and F is the Faraday constant. In engineering work, F is 96,485 C/mol. If the current changes during the cycle, replace I × t with the measured charge.
IUPAC defines current efficiency for a reaction as that reaction’s partial current density divided by the total current density. In plating language, it is the share of the electrode current that produces the intended deposit. Side reactions, commonly hydrogen evolution, are why η is below 1.
The equivalent weight M/n is already inside that equation. Divide by n once. A second division by valence counts the electrons twice and understates the mass.
The equation describes the gross metal produced by that cathode reaction. It assumes one reaction and one molar mass M. It does not describe electroless plating, where thickness follows the chemical reduction rate. It does not describe an alloy deposit with one pair of M and n, because more than one reduction is running. It also does not describe how much of that metal is still on the part after any later dissolution.
⚖️ From Mass to One Average Thickness
Average thickness over a stated area is
δ = m / (ρ × A)
ρ is the density of the deposit, and A is the area that equation is allowed to represent. Bulk nickel is often taken as 8.90 g/cm³ in plating tables. A porous deposit, or one that contains codeposited material, can have a lower density, so the same mass stands taller on the surface.
I/A is the average current density over that same area. It is not the current density at a corner or inside a recess.
🧪 An Illustrative Nickel Calculation
This example is arithmetic under stated assumptions. It is not a production record and not a bath certification.
Assume divalent nickel, Ni²⁺ + 2e⁻ → Ni, so n = 2 and M = 58.69 g/mol. At 100% cathode efficiency that reaction deposits about 1.095 g of nickel per ampere-hour, the factor used in the standard nickel plating handbooks (atomic weight near 58.7, two electrons, Faraday constant near 96,500 C/mol). With F = 96,485 C/mol the factor is 1.095 g/Ah to three decimals.
Now take an illustrative cycle:
- current 40 A, held constant
- time 1,800 s (0.50 h)
- cathode efficiency 0.95
- deposit density 8.90 g/cm³
- area 4.00 ft², converted as 929.03 cm²/ft², so 3,716 cm²
For this example, assume the stated area is the full area receiving the calculated deposit, with no additional deposition on conductive rack surfaces.
Charge is 40 × 1,800 = 72,000 C. Moles of electrons are 72,000 / 96,485 = 0.7462. Moles of nickel at full efficiency are half of that, 0.3731, because two electrons deposit one nickel atom. Mass at full efficiency is 0.3731 × 58.69 = 21.90 g. At 95% efficiency the mass is 20.80 g.
Volume is 20.80 / 8.90 = 2.337 cm³. Spread uniformly over 3,716 cm², the average thickness is 6.29 µm, which is 248 µin. The average current density is 40 A / 4.00 ft² = 10 A/ft².
Illustrative Nickel Cycle Under Stated Assumptions
Arithmetic for one hypothetical cycle. The area is the full area receiving the deposit, with none on conductive rack surfaces. Not a production record and not a bath certification.
| Item | Value |
|---|---|
| Half-reaction | Ni²⁺ + 2e⁻ → Ni, so n = 2 and M = 58.69 g/mol |
| Current and time | 40 A for 1,800 s (0.50 h), charge 72,000 C |
| Cathode efficiency | 0.95, applied to that full area |
| Deposit density | 8.90 g/cm³ |
| Area | 4.00 ft² (3,716 cm²), the full area receiving this deposit |
| Mass at 95% efficiency | 20.80 g |
| Average thickness | 6.29 µm (248 µin) |
| Average current density | 10 A/ft² |
That 6.29 µm is the average for 20.80 g of nickel spread over the 4.00 ft² this example defined. Dropping η from 0.95 to 0.80, with every other assumption fixed, lowers that average from 6.29 µm to 5.30 µm.
🧭 Current Efficiency Changes the Mass
Cathode current efficiency is the share of the cathode charge that produces the intended deposit. For the nickel processes covered in a standard nickel electroplating reference, cathode efficiency is described as commonly about 92–97%, while nickel anode dissolution is treated as essentially complete. A cathode efficiency below the value in the spreadsheet lowers the nickel mass on the cathode circuit. An anode efficiency near 100% while the cathode is a few percent lower tends to raise the nickel concentration of the bath. That concentration shift does not tell you why a recess is thin.
Changing one assumed efficiency value scales the calculated average mass. It cannot explain a spatial thickness pattern. Local efficiency can contribute to that pattern, because real cathode efficiency varies with local current density, chemistry, temperature, and mass transport. That variation belongs with current distribution. It is not a reason to revise the single spreadsheet factor until one recess matches.
For a nickel bath running at high efficiency, a few percent of hydrogen evolution moves the average thickness by about that same few percent. A twofold difference between an edge and a recess is a larger discrepancy than that average shift.
🏭 Current Distribution Changes the Location
Local current density follows the geometry of the part, the rack, the anodes, and the tank, then the electrochemical behavior of the bath. Edges, corners, and surfaces that face an anode draw more current. Recesses, holes, and shadowed faces draw less.
Classical work at the National Bureau of Standards separated the primary current distribution, fixed by shape and by the relative resistance of the current paths when polarization is ignored, from the metal distribution you actually plate. If cathode efficiency is the same at high current and at low current, local thickness follows local current. Polarization can pull the metal ratio closer to uniform than that primary current ratio. That improvement is what those papers call throwing power.
The same sources record the coupling that matters on the floor. When cathode efficiency is higher at low current density than at high current density, the area at low current receives a larger share of the metal than the current ratio alone would suggest. When efficiency is lower at low current density, the thin area is thinner still. Chromium plating is the familiar severe case: efficiency is poor, and it tends to fall further as current density falls, so recesses can be starved even when the ampere-hour total looks generous. The effect depends on the chemistry and operating conditions. Don’t assume nickel, copper, and chromium behave the same way.
Agitation and metal ion supply add another shift. A recess can be electrically able to plate and still be starved if the boundary layer is not renewed. That is a mass transport limit on local rate. It is not a revision of the Faraday constant.
Troubleshoot Plating Defects: Causes and Fixes treats the visible pattern: burning and heavy build where current density is high, skip or thin plate where it is low. Precision Electroplating: Hull Cell Analysis is a way to see a range of current density on one panel before you interpret a difficult part.
Metal that plates on hooks, thieves, and conductive rack surfaces is still cathode deposit. It consumes charge and it satisfies Faraday’s law for the cathode circuit. It does not appear in the thickness on the significant surface. A low reading on the part, with a believable total ampere-hour count, can be current that never reached the work you measured.
🔍 Why the Gauge and the Calculation Disagree
Compare like with like. Name which quantity each number represents before you decide that one of them is wrong.
Compare the Calculation With the Same Quantity the Gauge Reports
A weight gain, a Faraday average, a local reading, and an X-ray result answer different questions.
| Comparison | Question it answers | What it does not answer |
|---|---|---|
| Weight gain | What net coating mass remains on the surfaces you weighed? | The gross metal the cathode reaction produced, or the thickness at one location |
| Average thickness | What thickness does that mass imply over the area you declared? | The thickness at an edge or in a recess |
| Local thickness | What is the coating at one named place? | The average weighted by area over the part |
| X-ray reading | What coating mass per unit area is inferred from the X-ray measurement? | Linear thickness, which still requires an appropriate density assumption |
Weight gain — Weighing the work checks the net coating mass still on the surfaces you weighed. That is not the gross metal the cathode reaction produced. Chemical redissolution can remove deposit after it forms, so the scale can read low even when the charge and the average efficiency were right.
A coupon plated in the same circuit is not a shortcut around that distinction. Its geometry, area, and local current density can differ from the part and from the rest of the cathode. The coupon shows what that coupon did. It does not validate the Faraday mass balance for the load.
If the scale and the formula disagree, look at the charge that actually passed, the efficiency you assumed, whether deposit was later dissolved, and whether the weighed pieces are the whole cathode. Distribution can move metal from the significant surface onto the rack. Moving metal is not the same thing as destroying it. Dissolving it afterward changes the net mass you can weigh.
Average thickness — The usual errors are the area basis and the density basis. Total wetted area, significant surface, and a CAD area that ignores the rack are three different denominators. Because calculated thickness is inversely proportional to area, an error in the area basis directly biases the calculated average. Efficiency cannot be asked to absorb that error and still describe the bath.
Local thickness — A cross section or a reading from a small spot is one place on the distribution. Two points are not an average weighted by area, so an edge and a recess are not required to bracket the Faraday number. ASTM B487 covers local thickness by microscopical examination of a cross section. The result still depends on the microscope and on how the section was prepared.
X-ray thickness — ASTM B568 covers coating thickness by X-ray spectrometry. Treat the result as an inferred coating mass per unit area over the region the beam interrogates. That inference depends on the calibration, the coating and substrate model, the composition, and the measurement conditions. Linear thickness requires an appropriate density assumption. Faraday’s average uses a density as well. A shared density error can make the two numbers agree for the wrong geometrical thickness. Different density assumptions can make them disagree when the areal mass is consistent.
A rectifier trace that stays inside its control limits, as discussed in How to Set Control Limits for Plating & Metal Finishing, supports the current half of the charge record. It does not certify uniform thickness. Stable amperes through a poor rack still plate the edges.
The requirement language matters as much as the metrology. A minimum local thickness on a named surface can fail while the Faraday average over the whole part is exactly the number in the spreadsheet. The calculation was never a substitute for that local measurement.
✅ A Heavy Edge and a Thin Recess
Stay with the same hypothetical cycle. The calculation says 6.29 µm over the 4.00 ft² defined above. The edge measures substantially thicker. A recess falls below the local minimum on the drawing. Nothing in this section is a shop record. It is a way to separate a bad mass estimate from a local distribution problem before anyone changes the bath.
1. Is the charge record the charge that plated?
Forty amperes for 1,800 seconds is 72,000 C only if that current actually passed. Check whether the shunt sees the work or the whole bar. If the ampere-hours are wrong, the 20.80 g is wrong, and every thickness derived from it is wrong with it.
2. What did the 4.00 ft² include?
This example treats that area as the full area receiving the deposit, with no extra metal on conductive rack surfaces. If hooks, thieves, or the rack took part of the current, the part can run thin while the cathode mass is still about right. That is a problem of where the area boundary was drawn. It is not a reason to invent a new efficiency.
3. Was 0.95 a reasonable average for this bath?
One assumed efficiency scales the whole 6.29 µm. It cannot explain why the edge and the recess diverged. A weight gain near 20.80 g on the surfaces the calculation included supports the mass estimate and points toward where the metal went. A short weight gain points back to charge, average efficiency, dissolution after deposition, or metal that was never on the pieces you weighed. A coupon in the same circuit speaks only for the geometry and current density that coupon actually saw.
4. What did the specification require, and where was the gauge?
A minimum at a named recess can fail while the average over the declared area is exactly 6.29 µm. Confirm that the reading is the location the specification names.
5. What would separate the remaining causes?
A heavy edge and a thin recess make current distribution, electrical contact, and local efficiency worth investigating. The pattern does not establish which one caused the result. Rack and anode placement, shields, and contact resistance speak to distribution and contact. A Hull cell panel, or another check across a range of current density in this bath, speaks to whether efficiency falls where the current is low. Those are different tests.
Key Takeaway: Before changing a process because two numbers disagree, make sure those numbers were supposed to agree in the first place.
📋 What to Record Before You Interpret the Difference
Write the comparison down before you adjust the bath or the spreadsheet.
The Comparison Sheet
Capture the basis of the calculation and the basis of the measurement before either one is revised.
| Record | What to capture |
|---|---|
| Half-reaction | Including n, and whether the deposit is a single metal |
| Charge | Ampere-hours, or current and time, and whether the shunt sees the work or the whole bar |
| Efficiency | The value used, and whether it came from a net weight gain on a known area in this bath or from a generic table |
| Area | The area definition, in the same units as the thickness formula, including whether rack surfaces are in it |
| Density | The density used to convert mass to thickness, for both the calculation and any X-ray program |
| Bath | Identity, metal concentration, pH, temperature, and agitation, because those shift efficiency and distribution |
| Rack | Anode placement, thieves, and shields for that load |
| Measurement | Method, location, and whether the specification is an average, a minimum local thickness, or a mass |
Implementation Tip: When a reading misses the calculation, write down whether the evidence tested net mass, an average over a defined area, or a local reading at a named location.
⚠️ What a Thickness Number Does Not Prove
Agreement between a calculated average and one gauge reading does not prove corrosion life, hardness, adhesion, or alloy composition. Those depend on the deposit itself and on the specification that invoked thickness in the first place. A correct ampere-hour total also says nothing about an electroless cycle run in the same tank line, because that thickness was not produced by the rectifier charge.
🚩 Common Mistakes When the Numbers Disagree
❌ Dividing by valence twice. The equivalent weight M/n is already inside the mass equation. A second division understates the mass.
❌ Treating a coupon as the cathode balance. A coupon plated in the same circuit shows the deposit on that coupon. It does not validate the mass on the part.
❌ Closing the area on the workpiece while the rack was also plating. Metal on hooks, thieves, and conductive rack surfaces consumed charge. It will not show up in the thickness on the significant surface.
❌ Reading an X-ray thickness as a direct Faraday check. Match the area, the location, and the density basis first. Linear thickness from the X-ray reading still depends on that density, and on the calibration and measurement model behind the areal mass.
🔍 Keeping the Record Next to the Measurement
Lab Wizard Cloud is where a shop can keep dated bath analyses, tank readings, additions, and alerts in one history, with trends and an audit trail around those events. That history is the process context for a thickness discrepancy: what the bath and the logged tank conditions were when the load ran.
It does not measure coating thickness, determine cathode current efficiency, or calculate current distribution on a part. Thickness readings, weight gain checks, and the rectifier charge record remain evidence you bring to that history. Authorization of a thickness call stays with the specification and with the people who own the process.
🔗 Related Resources
- Electroplating Thickness Calculations (Faraday’s Law Made Simple). The worksheet side of this subject: how charge, efficiency, density, and area become one average thickness.
- Troubleshoot Plating Defects: Causes and Fixes. The visible pattern of burning and heavy build where current density is high, and skip or thin plate where it is low.
- Precision Electroplating: Hull Cell Analysis. A way to see a range of current density on one panel before interpreting a difficult part.
- How to Set Control Limits for Plating & Metal Finishing. What a rectifier trace inside its limits supports, and what it does not certify about thickness.
External Links
- Nickel Plating Handbook. The factor of about 1.095 g of nickel per ampere-hour at 100% cathode efficiency.
- Di Bari: Nickel Electroplating. The 1.095 g/Ah factor, a bulk nickel density of 8.90 g/cm³, and typical cathode efficiency for the nickel processes covered there.
- NBS: Throwing power in chromium plating. Primary current distribution and metal distribution, including the case where efficiency falls as current density falls.
- NBS Letter Circular 125: Throwing power in copper and nickel deposition. How polarization and efficiency shift metal distribution relative to the primary current ratio.
- Electrochemistry Encyclopedia: Electroplating. Cathode efficiency in the context of electrodeposition.
- ASTM B487. Local thickness by microscopical examination of a cross section.
- ASTM B568. Coating thickness by X-ray spectrometry.