I have a 250 VA UPS, and I have a couple of devices I want to run on it, a radio (7 watts) and a fan (55 watts). How do I calculate the required battery size (ampere-hours) (for a 12 V car battery)?
And to ensure the UPS is good for those devices, do I just calculate the sum of the load watts (55 watt + 7 watt < 250 * Power Factor) so this UPS can run those devices?
The battery size will affect only its duration. If you get a 1Ah battery it will discharge in approximately one hour if you draw 1A, half an hour if you draw 2A and so on.
The second formula is good, keep in mind that cheaper UPS have a square wave output instead of a sine wave, some devices may be affected. The radio might keep some noise from the UPS and the fan might not work well since these electric motors usually expect a sine as input. You are safe to try them anyway, no risk of frying anything.
To calculate the battery duration you should proceed as follows:
$$I=\frac{P}{V}$$
where P is power, in W, and V is voltage rms, in V. This formula is valid only if the load is resistive, in the AC domain things can get a bit more complicated, your appliances should report maximum current consumption on a label somewhere, use that value. After that:
$$T = \frac{C}{I}$$
Where T is duration, in hours, C is battery capacity, in Ah or A times hours, and I is current, in A. The computed time is not the actual duration you would get but it's the upper theoretical limit.
If you live in europe and your radio is approximately a resistive load it would draw about 40mA, so a 1Ah battery would last no more than 23h15m.
62 watts at 12 v -> 5.17 amps. 85% efficiency for converter -> 6.1 amps.
6.1 amps for an hour is 6.1 volt amp hours (VAh). You need to look at the VAh rating of the battery to determine how long it'll run your devices. A 100 VAh battery will run your stuff for 100/6.1 = 16.4 hours before it is utterly depleted.
However, you never want to run a car battery down below 50%, they tend to suffer irreversible damage, and won't recharge well. 6 to 8 hours max is as far as I'd be willing to go, and if you use 8, expect shortened battery life. For hard use, you'll want to consider a deep cycle battery. They're designed for the sort of abuse a 6 amp constant load can supply.
