A watt is not a watt-hour

The battery pack on my desk says 20,000 mAh in large letters. Its watt-hour rating is in much smaller letters. Naturally the large number is the one I remember when I am trying to work out whether something will run all afternoon.

A watt measures the rate at which energy is transferred. A watt-hour measures a quantity of energy: one watt sustained for an hour. A 10 W load running for six hours asks for 60 Wh before you allow for any losses.

Amp-hours need a voltage before they tell you energy. At a nominal cell voltage of 3.7 V, 20 Ah corresponds to 74 Wh. It does not imply that the pack can deliver 20 Ah at every output voltage. In particular, multiplying that cell-based rating by a USB output voltage would overstate the stored energy.

The nominal arithmetic is a starting point. The actual usable energy depends on the pack, its condition, temperature and converter. My label is not a test report. I have written the approximate watt-hours on a piece of masking tape so that I will at least start from the right number next time.

This is also why I wince when a spacecraft power source is described as producing “watts per hour”. It usually means watts. If someone really means a changing power level, watts per hour can be a perfectly sensible rate of change, but I would like them to say so.

The tea went cold while I was finding a pen. No useful energy was recovered.