Battery mAh versus Wh: different voltages, no comparison

mAh is charge, Wh is energy

mAh (milliamp-hours) is "how many mA for how many hours", an amount of charge. Wh (watt-hours) multiplies in the voltage to give energy: Wh = Ah × V. A 3,000mAh lithium-ion cell (nominal 3.7V) holds 11.1Wh; the same 3,000mAh in NiMH (1.2V) holds only 3.6Wh, a third of the energy.

Compare by mAh only between batteries of the same voltage; otherwise multiply by the nominal voltage to get Wh. Airline carry-on limits are written in Wh too: no restriction under 100Wh, airline approval from 100 to 160Wh (100Wh is 27,000mAh at 3.7V).

Where does a power bank's 10,000mAh go?

The stated capacity is the internal cells' value at 3.7V: 10,000mAh × 3.7V = 37Wh. At 5V that is 37Wh / 5V = 7,400mAh of charge. Nothing was lost; the current (charge) dropped because the voltage went up.

At 90% boost efficiency, 37 × 0.9 / 5 = 6,700mAh.

The phone also loses 10–15% stepping down, so the 5V-side charge needed for a 3,000mAh phone is 3,000 × 3.7 / 5 / 0.87 ≈ 2,550mAh. 6,700 / 2,550 ≈ 2.6 charges, not "10,000 / 3,000 = 3.3."

LDO versus DC-DC changes run time

An LDO (linear regulator) has input current equal to output current, and the voltage difference becomes heat. Drawing 50mA at 3.3V from a 3.7V lithium-ion cell also draws 50mA from the battery: 60 hours at 3,000mAh.

A DC-DC (switching) converter works on power: input current = output power / (input voltage × efficiency). At 90% the battery draws 3.3 × 0.05 / (3.7 × 0.9) = 49.5mA, nearly the same as the LDO.

The difference shows up when the output voltage is much lower than the input. Drawing 50mA at 1.8V from 3.7V, an LDO draws 50mA (60 hours) while a 90%-efficient DC-DC draws 1.8 × 0.05 / (3.7 × 0.9) = 27mA, or 111 hours, roughly double. With a small difference like 3.7V to 3.3V, the DC-DC's quiescent current (tens of µA to a few mA) can make the LDO last longer under light load.

Capacity you can't use: the cutoff voltage

A lithium-ion cell's rated 3,000mAh is measured from 4.2V down to 2.5–3.0V. An LDO outputting 3.3V with a 0.3V dropout can't hold the output once the battery falls below 3.6V, so capacity remaining below 3.6V is unusable.

Most of the capacity sits at 3.5–3.9V and only 20–30% remains below 3.6V, so a 3.6V cutoff gets 2,100–2,400mAh of the rated 3,000mAh.

The fixes are to lower the circuit's voltage, use a low-dropout LDO (0.1V or less), or use a buck-boost converter to run the cell down to 2.5V.

Temperature and discharge current shrink it further

• Low temperature. A lithium-ion cell holds about 80% of its room-temperature capacity at 0°C and 50–60% at −20°C, and its internal resistance rises, so it hits cutoff sooner.
• Discharge current. Rated capacity is measured around 0.2C (5-hour rate). At 1C it drops a few percent, and a lead-acid battery over 20% (Peukert's law).
• Pulse loads and coin cells. A CR2032 (225mAh, 3V) has an internal resistance of 10–40 ohm, so a 30mA radio pulse sags it by 0.3–1.2V and can trigger a reset. A parallel capacitor (100µF or more) can supply the pulse.
• Self-discharge. Lithium-ion loses 2–3% per month, NiMH 15–20% per month (15% per year for low-self-discharge cells), alkaline 2–3% per year.
• Aging. A lithium-ion cell drops to about 80% after 500 cycles, so calculate against 70–80% of initial capacity to guarantee run time at end of life.

Estimating with the calculator

Use the mAh-to-Wh calculator to get the battery's energy and divide by the device's power consumption (including conversion efficiency) for a rough run time. Multiplying in the unusable capacity, temperature, and aging, real run time is 50–70% of that. For charging cost, use the electricity cost calculator: a 37Wh power bank fully charged at 45Wh including losses, at 31 yen/kWh, costs about 1.4 yen.