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) is energy, obtained by multiplying in the voltage: Wh = Ah x V. A 3,000mAh lithium-ion cell (nominal 3.7V) holds 11.1Wh. The same 3,000mAh in a NiMH cell (1.2V) holds only 3.6Wh — a third of the energy.

Use Wh to compare what's actually inside a battery. Comparing by mAh alone is valid only between batteries of the same voltage. If a datasheet lists only mAh, multiply by the nominal voltage to get Wh before comparing.

This is why airline carry-on limits are written in Wh, not mAh: no restriction under 100Wh, airline approval required between 100 and 160Wh. At 3.7V, 100Wh corresponds to 27,000mAh.

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

A power bank's stated capacity is the value of its internal lithium-ion cells at 3.7V: 10,000mAh x 3.7V = 37Wh. Delivering that through USB at 5V requires boost conversion, and as charge that becomes 37Wh / 5V = 7,400mAh. It hasn't shrunk — the current (charge) has dropped because the voltage went up.

With a boost converter running at 90% efficiency, what actually comes out at 5V is 37 x 0.9 / 5 = 6,700mAh. Some products print this figure alongside the raw one, labeled something like "rated capacity: 6,700mAh."

The phone side has its own loss (10-15%) stepping 5V down to the cell's 3.7-4.2V for charging. The charge needed at the 5V side to charge a 3,000mAh phone is 3,000 x 3.7 / 5 / 0.87 ≈ 2,550mAh, so 6,700 / 2,550 ≈ 2.6 charges — not the "10,000 / 3,000 = 3.3 charges" naive division suggests.

LDO versus DC-DC changes run time

When a battery powers a device, the way its voltage is converted to the circuit's voltage changes how long it runs.

LDO (linear regulator). Input current equals output current; the voltage difference becomes heat. Drawing 50mA at 3.3V from a 3.7V lithium-ion cell also draws 50mA from the battery. At 3,000mAh, that's 60 hours. Efficiency is 3.3/3.7 = 89%, but it shifts with cell voltage: 79% at 4.2V, 94% at 3.5V.

DC-DC (switching converter). Conversion works on power, so input current = output power / (input voltage x efficiency). Under the same conditions at 90% efficiency, the battery draws 3.3 x 0.05 / (3.7 x 0.9) = 49.5mA — nearly identical to 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 still draws 50mA (60 hours), while a 90%-efficient DC-DC draws 1.8 x 0.05 / (3.7 x 0.9) = 27mA, giving 111 hours — roughly double. Conversely, with a small voltage difference like 3.7V to 3.3V, the DC-DC's fixed overhead (tens of µA to a few mA of quiescent current) 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 discharging from 4.2V down to 2.5-3.0V. But if the circuit's LDO outputs 3.3V with a 0.3V dropout, it can't hold the output once the battery drops below 3.6V. Whatever capacity remains below 3.6V is simply unusable.

Most of a lithium-ion cell's capacity sits in the 3.5-3.9V range of its discharge curve, and only 20-30% remains below 3.6V. So a design with a 3.6V cutoff only gets to use 2,100-2,400mAh of the rated 3,000mAh.

The fixes are: lower the circuit's operating voltage (3.3V to 3.0V, or 1.8V), use a low-dropout LDO (0.1V or less), or use a buck-boost converter to run the cell all the way down to 2.5V. In a battery-powered design, "down to what voltage does it still run" translates directly into run time.

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. Internal resistance also rises, so under a heavy load the voltage sags further and the cell hits cutoff sooner.
• Discharge current. Rated capacity is measured around 0.2C (5-hour rate). At 1C (1-hour rate) capacity drops a few percent; a lead-acid battery can drop over 20% (Peukert's law). At very low currents, you can pull out more than the rated value.
• Pulse loads and coin cells. A CR2032 (225mAh, 3V) has an internal resistance of 10-40 ohm; a radio module pulling a 30mA pulse can sag it by 0.3-1.2V. Even with plenty of average current margin, a voltage sag during the pulse can trigger a reset. A parallel capacitor (100µF or more) can supply the pulse instead.
• 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. For equipment left idle for a year or more, factor this into the run-time calculation.
• Aging. A lithium-ion cell drops to about 80% of capacity after 500 cycles. If you need to guarantee run time at end of life, calculate against 70-80% of the initial rated capacity.

Estimating with the calculator

Use the mAh-to-Wh calculator to get the battery's energy, then divide by the device's power consumption (voltage x current, including conversion efficiency) for a rough run-time estimate. From there, multiply in the unusable capacity (cutoff voltage), temperature, and aging factors — it's safe to assume real run time comes out to 50-70% of that rough number.

You can estimate charging cost with the electricity cost calculator. Fully charging a 37Wh power bank at 45Wh including charging losses, at 31 yen/kWh, costs about 1.4 yen.