Calculating Ah from Watts

To calculate amp-hours from watts, divide the watts by the battery voltage. A 100W device on a 12V battery draws about 8.33A, so it consumes 8.33Ah for every hour it runs.

Let me show you where that comes from, with a real example.

On my van, I have a 12V 100Ah battery.

Let’s say I have a 100W hair dryer that I run through a power inverter. For how many hours can I run it, before the battery capacity ends?

The formula

Power, voltage and current are tied together by this formula:

W = V × A

Watts equal volts times amps. We know the watts (100W) and the volts (12V), so we solve for amps:

A = W / V
100W / 12V = 8.33A

The hair dryer pulls 8.33A from the battery. Run it for one hour and you’ve used 8.33Ah of capacity.

1 watt-hour is 1 watt of power expended for 1 hour

The battery holds 100Ah, so:

100Ah / 8.33A = 12 hours

If I had a device that consumed 200W, the current would double to 16.66A, and I could run it for 6 hours.

Real batteries don’t give you 100%

This assumes I can consume 100% of the battery’s capacity. That’s almost true with a LiFePO4 battery, but not for regular lead-acid batteries.

A lead-acid battery should not be discharged below 50%, or its lifespan drops fast. So a 100Ah lead-acid battery really gives you about 50Ah of usable capacity. My hair dryer would run for 6 hours, not 12.

Don’t forget the inverter

The inverter also eats some power. A typical inverter is around 90% efficient, so to deliver 100W to the hair dryer, it pulls about 111W from the battery:

100W / 0.90 = 111W
111W / 12V = 9.26A
100Ah / 9.26A = 10.8 hours

The realistic answer for my LiFePO4 setup is closer to 10-11 hours than 12.

One mistake to watch for: don’t use the amps printed on the device label. A 100W appliance rated for 230V mains draws only 0.43A at 230V, but that number is useless here. What matters is the current on the battery side, at 12V. Always convert from watts using the battery voltage.