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How large is your smartphone's battery? Most people would answer that question in terms of milli-Ampere hours (mAh). This shouldn't be surprising considering that it is the consumer electronics industry's metric of choice for measuring battery capacity. There's just one problem though -- mAh is not a measure of energy, which can lead to confusion when consumers are trying to compare different battery packs.
The metric of mAh simply states how long a battery can provide power at a given current draw. Say a battery is 4,000 mAh, or 4 Ah. This means that if we expect to draw an average of 1 Ampere of current from the battery, a full charge will last us 4 hours. This is useful information, but it leaves out one crucial detail: the voltage that the current is delivered at.
In order to understand why this matters, ask yourself this question: Does current or voltage power your devices? This is actually a trick question -- both current and voltage matter equally since Power (Watts) = Current (Amps) * Voltage (Volts). The voltage that the current is delivered at makes the difference between being able to power a single smartphone and being able to power an entire neighborhood. Going further, electrical energy is simply electrical power integrated over time (typically in hours), yielding the unit of electrical energy: the Watt-hour (Wh). This is the unit that is used to measure energy on your power bill, typically 10-30 cents per kilo-Watt-hour depending on where you live. Now you can see why the unit "Ah" is not so descriptive, in order to figure out how much energy it contains we have to multiply it by the battery's nominal voltage to turn Amp-hours into Watt-hours; and depending on the voltage it could contain enough energy to power an LED for a day, or an entire city for a day, but we would have no way of knowing with just the Ah rating.
Of course the reason that Ah is even passable as a metric for comparing batteries is because most of the battery packs in consumer electronics have the same nominal voltage -- one lithium cell in series which gives about 3.7 V. This is the underlying assumption that allows you to compare the batteries of two different smartphones using their mAh ratings, of course if the nominal voltage is the same then Amp-hours becomes a useful proxy for comparing the energy capacity of the two batteries. But this whole ridiculous situation begs the question: Why not just Watt-hours instead to measure energy capacity?!?!? Watt-hours is a measure of energy, whereas Amp-hours is not. There is no good reason to use Amp-hours over Watt-hours, it is simply a situation of a confusing status quo having too much momentum to be corrected.
So please, stop using Amp-hours to measure a battery's energy capacity, and report it in Watt-hours instead.