Volts, amp-hours and watt-hours: converting between them

Amp-hours alone can't be compared between two batteries. Watt-hours can. The conversion is one multiplication.

What each unit says

An amp-hour (Ah) is a measure of electric charge. One amp-hour is the charge moved by a steady current of one ampere flowing for one hour¹. Battery capacity is usually stated in amp-hours².

Voltage is the push behind that current. A battery label usually gives a voltage next to its amp-hours.

A watt-hour (Wh) is energy, the same kind of unit as the kWh on the kW versus kWh page.

The sum

Electric power is current times voltage, written as P = IV³. Run that for an hour and you get energy. So:

watt-hours = volts × amp-hours

Say a label reads 48 V and 100 Ah. Multiply to get 4,800 Wh. Divide by a thousand and you get 4.8 kWh, because the kilowatt-hour is the watt-hour with a metric prefix⁴. Those numbers are an invented example, only to show the steps.

Why two batteries need the same scale

Take two invented labels: one says 12 V and 200 Ah, the other says 48 V and 50 Ah. The amp-hours look very different. Multiply each and both come to 2,400 Wh, using the same sum as above³. Same energy, different packaging.

Voltage is the missing piece³. A higher-voltage battery can hold the same energy with fewer amp-hours, since each amp-hour carries more energy at a higher voltage. Comparing 100 Ah at one voltage with 100 Ah at another tells you very little. Only the product of the two means anything.

That's why amp-hours alone mislead. When you compare the energy capacities of battery products with different internal chemistry or cell layouts, a simple amp-hour rating is often insufficient¹.

What the sum leaves out

The voltage on the label is a nominal value. Battery voltage generally varies during discharge, so an average or nominal value is used to approximate the energy¹. The result is an estimate, not a measured figure.

Real energy can differ from the label sum. Here's why.

• The amp-hour rating is tied to test conditions, such as a slow discharge at a set temperature².
• Not all of the rated capacity is usable, because of the held-back band covered in this earlier note.
• Losses happen between charging and use, as in round-trip efficiency.

If a spec sheet already gives watt-hours or kilowatt-hours, use that figure, and read the maker's note on how it was measured.

Safety note

This is arithmetic for comparing labels. It isn't a guide to building or changing a battery. Don't connect cells or modules together yourself. Anything beyond the plug-in use the maker describes in the manual is work for the maker or a licensed electrician.