Coulombs to Millicoulombs

Coulombs to millicoulombs: the exact conversion

A coulomb is the SI unit of electric charge and a millicoulomb (mC) is one thousandth of one. The prefix milli belongs to the SI prefix set defined in the BIPM SI Brochure (9th edition, 2019) and applied in United States practice through NIST's SI prefixes page and NIST SP 811 (2008). Since prefixes are definitions, the conversion never rounds:

• 1 C = 10³ mC = 1,000 mC
• 1 mC = 0.001 C = 1 × 10^-3 C
• 1 mC = 1,000 µC and 1 µC = 0.001 mC

Multiply coulombs by 1,000 to get millicoulombs; divide millicoulombs by 1,000 to go back. Millicoulombs occupy a useful middle ground. One whole coulomb is a lot of charge for a single event, while microcoulomb counts get awkward once a device moves serious charge. The amount a defibrillator stores, the amount a camera flash dumps and the amount a plating bath moves in a minute all land in the tens or thousands of millicoulombs, which is why this page pairs the conversion with battery, capacitor and electrolysis examples instead of static electricity ones.

Why 1 mAh equals 3.6 C

A coulomb is one ampere flowing for one second: 1 C = 1 A × 1 s. Battery capacity is printed in milliamp hours, so connecting the two produces a fixed factor: 1 mAh = 0.001 A × 3,600 s = 3.6 C, which is 3,600 mC. The factor is exact, not an approximation, because both the ampere and the hour are defined quantities, the hour being 3,600 seconds by definition.

Worked example: a phone battery rated at 2,500 mAh stores 2,500 × 3.6 = 9,000 C, or 9,000,000 mC. Run the arithmetic the other way for a load: drawing 300 mA for one hour moves 0.3 × 3,600 = 1,080 C, which is 1,080,000 mC and consumes 300 mAh of the cell. The mAh figure and the coulomb figure carry the same information, and the converter prints both at once so a datasheet in C compares cleanly against a battery spec in mAh.

Cell ratings move fast, so the same factor handles them all:

Coulomb counting: how a fuel gauge uses millicoulombs

Battery gauges estimate remaining capacity by coulomb counting: they integrate current in and out over time, ΔQ = I × Δt, and keep a running total in coulombs or directly in mAh, the same accounting with the 3.6 factor applied. Every 3,600 mC that leaves the cell is 1 mAh gone. Drift creeps in through sensor error and through the fact that the counter never sees the chemistry, which is why gauges recalibrate against voltage and full cycles.

Check a row: 2 A for 45 minutes is 2 × 2,700 s = 5,400 C, and 5,400 ÷ 3.6 = 1,500 mAh. On the 2,500 mAh cell from the previous section, that leaves 1,000 mAh, or 3,600 C, in the tank. The same integration runs in reverse for charging, and a gauge that is off by 1 percent of the current loses 25 mAh, or 90 C, over a full discharge of that cell. Under heavy drain the cell's internal resistance wastes part of the voltage before any current reaches the terminals, so the gauge still counts every coulomb while the device quits earlier than the arithmetic suggests. A coulombmeter keeps a running total of ampere hours instead, and a shunt resistor in the return line is what lets the gauge watch the current. Calendar aging and self discharge sneak past any integration method, so a good fuel gauge blends the coulomb count with a voltage lookup and a temperature correction. Peukert losses make a hard discharge yield fewer ampere hours than a gentle one, and a battery management chip stores the counted total in its own memory so a reboot does not erase the history. State of charge, state of health and cycle count all fall out of the same integration once the firmware knows the pack's rated capacity. Hardware has caught up too: a Hall-effect sensor or a sense resistor feeding an analog integrator replaces the old silver coulometer, the electrochemical cell chemists once wired in series to totalize a charge by weighing deposited silver.

Capacitor energy: E = ½ C V² and the 400 mC shock

Charge and energy travel together, but they are not the same number, and a medical defibrillator makes the difference concrete. Storage capacitors in defibrillator designs typically run around 200 µF, with teaching sources quoting a 100 to 300 µF range; external shocks span 50 to 400 J. Take a 200 µF capacitor charged to 2,000 V:

• Charge: Q = C × V = 200 µF × 2,000 V = 0.4 C = 400 mC
• Energy: E = ½ C V² = ½ × 200 µF × (2,000)² = 400 J

Same capacitor, same voltage, two different numbers, and only the joule figure says what the shock delivers. Sources: a McMaster University defibrillator lecture (capacitor typically 200 µF, delivered energies 50 to 400 J externally) and anaesthesia course notes from the University of KwaZulu-Natal (storage capacitors 100 to 300 µF, monophasic devices set to 360 J). Supercapacitor modules sit at the far end of the same scale. A single 1 F cell charged to 2.7 V holds 2.7 C, which is 2,700 mC. Wire ten of them in series and the module reaches 27 V while still holding 2,700 mC, because series connection raises the voltage and leaves the charge untouched, and a balancing circuit keeps that stack from drifting as the cells age. Electrolyte chemistry sets how much charge leaks away on a shelf, and the impedance of the porous separator limits the current a cold module can push.

A camera flash: 60 mC in a millisecond

The same mathematics scales down to a disposable camera. Photoflash storage capacitors are typically 200 to 300 µF, rated at 330 V and charged to about 300 V, with flash energies near 10 watt seconds, per the long running strobe repair FAQ maintained by Samuel Goldwasser (repairfaq.org, version 2.71, 2022). Take the low end, 200 µF at 300 V:

• Charge: Q = 200 µF × 300 V = 0.06 C = 60 mC
• Energy: E = ½ × 200 µF × (300)² = 9 J

Nine joules is 2.5 millionths of a kilowatt hour, since 1 kWh is 3.6 MJ, and the 60 mC leaves through the xenon tube in roughly a millisecond, which is why the light is so bright for its size. For scale against the battery section, 60 mC is 60 ÷ 3,600 = 0.0167 mAh, a rounding error next to the 2,500 mAh cell, yet the flash empties it in a millisecond while the phone spends hours draining the same amount. The charge number and the speed number together describe the event; either one alone undersells it. A tiny inverter inside the camera boosts the 1.5 V cell up to the charging voltage, which is why the flash needs a few seconds between shots. Studio strobes scale the same recipe: a bigger electrolytic bank, a longer recharge whine and a modelling lamp that bleeds a little current between pops.

Electroplating by the numbers: Faraday's law

Electrolysis converts charge directly into mass, and the exchange rate is the Faraday constant, F = 96,485.33212 C per mole of electrons. The value is exact in the current SI because it is the elementary charge times Avogadro's constant, both fixed by definition, and it is tabulated on NIST's constants pages. For a metal ion that takes z electrons per atom, the mass deposited is m = Q × M ÷ (z × F), with M the molar mass.

Worked example: copper plating at 0.5 A for 2 minutes. The charge passed is Q = 0.5 × 120 = 60 C, which is 60,000 mC. Copper (Cu²⁺, M = 63.546 g/mol) needs z = 2, so m = 60 × 63.546 ÷ (2 × 96,485.33212) = 0.01976 g, under 20 mg.

At production currents the numbers leave millicoulombs quickly. The same 0.5 A run for an hour passes 1,800 C, or 1,800,000 mC, and plates about 593 mg of copper, thirty times the short run. That is the point of the prefix ladder: it is the same coulomb throughout, rescaled to whatever size the job happens to be. Silver, zinc and nickel follow the same law with their own molar masses and valences. Plating line operators size a rectifier the same way: work out the charge each workpiece needs, then divide by the current to get the time. A rack needing 120,000 mC per bracket, run at 2 A, sits in the tank for 120,000 / 1,000 / 2 = 60 seconds, and the same rack at 20 A finishes in 6 seconds with the same deposit. Quality labs quote charge passed per unit area in the unit that keeps the digits readable, and the converter handles the rescaling.

Conversion chart: C, mC, µC and mAh

The table below ties the prefixes to the battery unit. Every entry is exact; the mAh column is the charge divided by 3.6, so its displayed digits are rounded for reading only:

One Faraday of charge is 96,485 C, about 26,801 mAh, which is why a battery holding a couple of thousand mAh moves roughly a tenth of a mole of electrons across its terminals over a full discharge. Going from C to mC multiplies by 1,000, and from mC to mAh divides by 3,600. Any two columns are one fixed factor apart, so a forgotten factor produces an error of exactly one thousand or exactly 3,600, and those signatures are easy to spot.

Mistakes worth a factor of a thousand

• Swapping m and M. Lower case m is milli, 10^-3; upper case M is mega, 10⁶. A millicoulomb and a megacoulomb differ by a factor of a billion.
• Treating mAh and mC as interchangeable. They differ by 3,600: 1 mAh is 3,600 mC, so the 400 mC defibrillator charge is 0.1111 mAh, not 400.
• Forgetting to convert minutes to seconds. Q = I × t needs seconds: 0.5 A for 2 minutes is 60 C because 120 s went into the formula, not 2.
• Dropping the one half in E = ½ C V². Q = C × V gives charge; multiplying charge by voltage once more without the half overstates the stored energy by a factor of two.
• Rounding 3.6 early. The mAh to C factor is exact, and carrying it as 4 turns a 2,500 mAh cell into 10,000 C instead of 9,000 C, an 11 percent error before any measurement happens.

A thirty second check catches all five: convert to coulombs first, apply one prefix at a time, and confirm the result against Q = C × V for capacitors or I × t for currents. Every example on this page passes that check, and any number that fails it is wrong by a known factor. Tolerance stacks on top: a 10 percent capacitor rating moves both Q and E together, so quote worst cases when it matters.