mAh vs Wh: How to Read a Battery's Capacity

A battery's mAh figure tells you how much electric charge it can supply, while its Wh figure tells you how much energy it holds. To compare two batteries fairly, convert mAh to Wh by multiplying the capacity in amp-hours by the battery voltage. This article explains both units, shows the conversion, and says why the watt-hour number is the one that appears in airline rules.

What mAh measures

Wikipedia explains that the ampere-hour measures electric charge, and that one ampere-hour equals 3,600 coulombs, the charge carried by a steady current of one ampere flowing for one hour. A milliampere-hour, or mAh, is one thousandth of that, so 1,000 mAh equals 1 Ah and 3.6 coulombs per mAh.

The article stresses that amperes measure current only, not power. A figure in mAh therefore does not say how much work a battery can do until you also know its voltage.

What Wh measures

A watt-hour is a unit of energy: the energy delivered by one watt of power sustained for one hour. Wikipedia's article on the kilowatt-hour makes the same point for its larger unit, that a kilowatt-hour equals 3.6 megajoules and that a kilowatt measures power while a kilowatt-hour measures energy. It also calls the phrase watts per hour a misuse.

Energy depends on both charge and voltage, which is why a watt-hour figure works across different batteries.

The conversion

Wikipedia gives the idea that capacity in ampere-hours assumes a commonly known nominal voltage. Energy can be approximated by multiplying the ampere-hours by that nominal voltage. In formula form: Wh = (mAh divided by 1,000) times volts.

Here is a worked example. A phone battery rated 5,000 mAh at a nominal 3.7 V has 5 Ah. Multiply 5 by 3.7 and the result is 18.5 Wh. The 3.7 V figure is a typical label value for a single lithium-ion cell, but the actual rating is printed on the battery or in its specification, so use that number.

• Divide mAh by 1,000 to get Ah.
• Multiply Ah by the nominal voltage in volts.
• The result is the energy in Wh.
• Divide Wh by 1,000 if you want kWh.

Why voltage changes the answer

Wikipedia's example shows the effect. One ampere-hour at 1.5 V gives roughly 1.5 Wh, while one ampere-hour at 12 V gives roughly 12 Wh, eight times the energy for the same mAh figure. Comparing two power banks by mAh alone can mislead if one uses a different internal or output voltage. A battery's rating on the label might be quoted at the cell voltage, while the output is at a different voltage.

The same article gives an electric car example. A battery of 96 cells at 3.6 V and 60 Ah comes to 20,736 Wh, or about 18 kWh of usable energy once reserve is accounted for. The sum is 96 times 3.6 times 60.

Limits of the rating

The Wikipedia article warns that a simple ampere-hour rating is often not enough to compare batteries of different types or layouts. Real output depends on losses, discharge limits, current limits and Peukert's law, which says that the usable capacity falls when the battery is drained at a higher current. Voltage also drops as a battery discharges, so a nominal voltage is an approximation, not an exact value.

Why airlines use Wh

The International Air Transport Association's lithium battery page says that lithium batteries can be carried depending on configuration and watt-hour rating for rechargeable types, or lithium content for non-rechargeable ones. It also states that spare batteries are not allowed in checked baggage. The limits for passengers are on a separate guidance page, which we did not read, so check your airline or the national aviation authority for the current thresholds.

Because the rule is written in watt-hours, a traveller with a power bank labelled only in mAh may need to do the conversion above, using the voltage printed on the label. Many products print the watt-hour rating directly, which avoids the sum.

Sources

• Ampere hour, Wikipedia
• Kilowatt-hour, Wikipedia
• Lithium batteries, IATA