Battery Capacity: Why mAh and Wh Tell Different Stories

A 20,000 mAh power bank sounds like a bigger battery than a 12,000 mAh e-bike pack. It holds one sixth of the energy. Neither label is lying — the comparison itself is broken, because milliampere-hours only mean something once you know a second number the marketing rarely leads with: voltage. This guide covers what mAh actually counts, why watt-hours are the unit that compares batteries honestly, and how to get from either figure to the answers people actually need — whether a pack can fly, how long it runs a load, and how big a storage bank has to be.

Charge and energy are not the same quantity

A milliampere-hour is a unit of electric charge. One ampere-hour is the charge a current of one amp delivers in one hour, and a milliampere-hour is a thousandth of that, so a 5,000 mAh cell can in principle supply 5 A for an hour or 1 A for five hours. What charge cannot tell you is how much work gets done along the way, because that depends on how hard each unit of charge is pushed — which is the voltage.

A water analogy holds up well here. Charge is the litres in the tank; voltage is the height the water falls from; energy is what the falling water can do. Two tanks holding identical litres are worlds apart if one sits on a rooftop and the other at knee height, and two batteries holding identical milliampere-hours are just as far apart when one runs at ten times the voltage of the other.

The conversion runs through nominal voltage

Wh = (mAh ÷ 1,000) × nominal voltage

The voltage in that formula is the nominal one — the manufacturer's representative mid-discharge value, not the fully charged peak and not whatever a built-in converter outputs. Typical nominals: 3.7 V for a lithium-ion cell, 3.2 V for LiFePO4, 12 V for a lead-acid block. For a 5,000 mAh phone cell: 5,000 mAh ÷ 1,000 = 5 Ah, and 5 Ah × 3.7 V = 18.5 Wh.

This is more than a physics convention. US federal regulation (49 CFR 171.8) defines a lithium-ion battery's watt-hour rating as exactly this product — rated ampere-hours times nominal voltage — which is the definition the battery capacity calculator implements and cites. Watt-hours are what datasheets, customs declarations and aviation rules mean when they say "capacity."

Four labels, two orderings

Put four common batteries side by side and watch the ranking change with the unit:

By mAh, the e-bike pack ranks below the power bank — 12,000 against 20,000. By energy it holds exactly six times as much: 444 Wh ÷ 74 Wh = 6. The explanation is in how the pack is built. That e-bike battery is forty identical 3.7 V, 3,000 mAh cells in a 10S4P arrangement: ten in series multiplies voltage, 10 × 3.7 V = 37 V, while four parallel strings multiply charge, 4 × 3,000 mAh = 12,000 mAh. Each cell stores 3.7 V × 3,000 mAh = 11.1 Wh, and forty of them store 40 × 11.1 Wh = 444 Wh — agreeing with the pack-level product 37 V × 12 Ah = 444 Wh. Series wiring is invisible to the mAh label; energy sees both directions.

The distortion scales, too. In charge terms the leisure battery (100 Ah = 100,000 mAh) looks 100,000 ÷ 5,000 = 20 times the phone cell; in energy terms it is 1,200 ÷ 18.5 ≈ 65 times. And even matched ampere-hours mislead across chemistries: a 12 V lead-acid block at 100 Ah stores 100 × 12 = 1,200 Wh, while a LiFePO4 block of the same 100 Ah runs at a 12.8 V nominal and stores 100 × 12.8 = 1,280 Wh — an extra 80 Wh hiding in a voltage difference the ampere-hour figure cannot see.

The 5 V trap, and the threshold that rides on it

Power banks add a twist: the cells inside are nominally 3.7 V, but the USB socket delivers 5 V through a boost converter. Multiply by the socket voltage and a 20,000 mAh bank appears to be 20 Ah × 5 V = 100 Wh. The rating is defined at the cell's nominal voltage instead: 20 Ah × 3.7 V = 74 Wh.

The gap between those two answers is not academic. The US Department of Transportation's passenger rules — 49 CFR 175.10(a)(18), the section the battery capacity calculator applies and cites — draw their lines at exactly 100 Wh and 160 Wh: at or below 100 Wh a lithium-ion battery needs no special approval, between 100 and 160 Wh it needs the operating carrier's approval with at most two such spares per person, and above 160 Wh the passenger exception does not apply at all. Use the converter's 5 V and a comfortably compliant 74 Wh pack lands, on paper, right on the 100 Wh line. In every band, spares belong in carry-on with short-circuit protection, and airlines may impose stricter rules than the regulation.

From watt-hours to hours

Once capacity is in energy units, runtime is one division: hours = watt-hours ÷ load watts. Run a 50 W compressor fridge from the 1,200 Wh leisure battery and the ideal figure is 1,200 ÷ 50 = 24 hours. The charge route agrees, which is a useful cross-check: the load draws 50 W ÷ 12 V = 4.17 A, and 100 Ah ÷ 4.17 A ≈ 24 hours.

Treat 24 hours as a ceiling, not a forecast. An inverter between battery and load takes a cut and raises the current the battery must supply; lead-acid gives up capacity when discharged fast (the Peukert effect); cold shrinks what is available; and low-voltage cut-offs trip before the last ampere-hour is out. The battery life calculator takes the first two as named, editable inputs with neutral defaults — a system efficiency for the inverter, a Peukert exponent for the rate derating — so you can see what each correction costs instead of receiving one blended guess. Cold and cut-off behaviour it deliberately does not model, and it says so beside the result: those call for spare margin, not arithmetic.

Depth of discharge: the capacity you are allowed to use

The rated number is not an invitation to use all of it. Depth of discharge — the fraction of capacity actually cycled — is a manufacturer's specification traded against cycle life, and it varies by chemistry and product. Hold that lead-acid leisure battery to a 50 percent depth of discharge and only 1,200 × 0.50 = 600 Wh are in play, so the fridge's 24 hours drops to 600 ÷ 50 = 12 hours.

This is why storage sizing runs the arithmetic backwards. The off-grid convention, as the solar battery sizing calculator applies it, is: nominal capacity = daily backed-up energy × days of autonomy ÷ depth of discharge ÷ round-trip efficiency. Suppose a home needs 8 kWh per day covered for one day, on a battery rated for 80 percent depth of discharge with 90 percent round-trip efficiency: 8 ÷ 0.80 = 10 kWh, then 10 ÷ 0.90 ≈ 11.1 kWh of nominal capacity. The two divisors compound — 0.80 × 0.90 = 0.72, and 1 ÷ 0.72 ≈ 1.39 — so the bank must be about 39 percent larger than the load it protects. Buy on the nameplate without that gross-up and the shortfall surfaces as thin autonomy, or as a battery cycled deeper than its warranty allows.

Reading a label in the right order

The working sequence, whatever the battery: find the nominal voltage first, convert the charge figure to watt-hours, and only then compare, plan or size. Milliampere-hours remain perfectly serviceable between cells at the same voltage — one 3.7 V phone cell against another — but the moment voltages differ, only watt-hours rank batteries by what they actually store. Divide watt-hours by load watts for a runtime ceiling; apply depth of discharge and conversion efficiency before trusting the answer with anything that matters.

That habit of printing the arithmetic beside the answer runs through the whole Quanta collection, well beyond the battery tools. And where this guide stops — chemistry-specific cycle-life trade-offs, charge-time arithmetic, a label that stays stubborn even with the nominal voltage in hand — the contact page picks up, going straight to the people who maintain these calculators.

Sources

• 49 CFR §175.10 — U.S. passenger rules for lithium batteries (the 100 Wh and 160 Wh thresholds)
• 49 CFR §171.8 — hazardous-materials definitions, including watt-hour rating
• FAA PackSafe — lithium batteries in carry-on and checked bags
• OpenStax University Physics Vol. 2, §9.5 — electrical energy and power