Ampere-Hour Calculation For Electroplating And Battery Testing: Faraday’s Law, Thickness And Capacity

The Basic Formula

Ampere-hours are current multiplied by time. With a steady 50 A for 2 hours, the charge is 100 Ah. When the current varies, which it nearly always does, the meter adds up current × time continuously, so the total is still correct. If you are new to this, start with what an ampere-hour meter is and how it works.

• Ah = A × hours (for constant current)
• 1 Ah = 60 A·min = 3,600 coulombs

How Many Grams Does One Ampere-Hour Deposit?

Faraday’s law says the mass of metal deposited is proportional to the charge passed. For any metal, grams per Ah at 100% efficiency = atomic mass × 3,600 ÷ (valency × 96,485). Worked out for common plating metals:

Efficiency figures are typical ranges; your bath supplier’s data sheet is the better source for your own process.

From Thickness to Ampere-Hours: Worked Example

Say you need 10 µm of nickel on parts with a total area of 10 dm², at 95% efficiency.

1. Mass needed = thickness (µm) × density × area (dm²) ÷ 100 = 10 × 8.9 × 10 ÷ 100 = 8.9 g
2. Ah needed = mass ÷ (g per Ah × efficiency) = 8.9 ÷ (1.095 × 0.95) = 8.6 Ah
3. Time at 4 A/dm² (40 A total) = 8.6 ÷ 40 = 0.21 h, about 13 minutes

Set the Ah meter preset to 8.6 Ah and the cycle will stop at the right coating weight even if the current wanders between 35 and 45 A. A timer set to 13 minutes would not.

A handy shortcut

Work out Ah per µm per dm² once for each bath. For the nickel above it is 8.6 ÷ (10 × 10) = 0.086. After that, preset = 0.086 × thickness × area. For example, 15 µm on 6 dm² needs 0.086 × 15 × 6 = 7.7 Ah.

Why real parts don’t match the calculation exactly

• Area is underestimated. Count both sides, holes, threads and any exposed rack area.
• Current distribution is uneven. Edges and corners get more, recesses get less. The calculation gives the average, not the minimum.
• Efficiency changes with bath temperature, metal concentration and current density.

The practical fix: calculate first, plate a trial batch, measure thickness at the thinnest critical point, then adjust the Ah preset. Once set, Ah control keeps it repeatable. For a precious-metal example, see why gold plating thickness varies batch to batch.

Using Ampere-Hours to Test Battery Capacity

A battery’s rated capacity is the Ah it should deliver at a stated discharge rate, usually the 10-hour (C10) or 20-hour (C20) rate, down to a specified end voltage. To check it:

1. Charge the battery fully and let it rest.
2. Discharge at the rated current: a 150 Ah C10 battery is discharged at 15 A.
3. Stop at the manufacturer’s cut-off voltage, typically about 1.75 V per cell for lead-acid at the 10-hour rate.
4. Read the Ah delivered and divide by the rating.

Example: the 150 Ah battery reaches cut-off after 8 h 20 min at 15 A. That is 125 Ah, or 83% of rated capacity. Batteries are commonly replaced once they fall below 80%.

Things that change the result

• Discharge rate. Discharging faster than rated gives fewer Ah. Always test at the rate on the datasheet.
• Temperature. A cold battery delivers less. Correct to the datasheet’s reference temperature.
• Constant current. If the load current drifts, an Ah meter still gives the correct total, while hours × nominal current does not.

For standby systems, see how to test UPS battery capacity.

Charge Factor: Ah In vs Ah Out

To fully recharge a lead-acid battery you must put back more Ah than you took out, typically 10–20% more, because some current is lost to gassing and heat. Lithium-ion cells are far more efficient, close to 1:1. Meters with separate charge and discharge counters show both numbers, so you can see the actual ratio instead of guessing.

Quick Checklist

• Use the full plated area, not just the visible face
• Use your bath’s actual cathode efficiency
• Confirm the preset unit: Ah or A·min
• Verify with a thickness measurement on the first batch
• For batteries, test at the rated discharge current and correct for temperature