# Battery Size for a UPS

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.

• is it possible to calculate how many Ah it draws from the watts? – user41468 May 9 '14 at 11:39
• from the watts you calculate the current, in A, then capacity in Ah divided by current in A results in theoretical duration. A device does not draw Ah, it draws A. – Vladimir Cravero May 9 '14 at 12:03
• how? can you give me an equation to do so? – user41468 May 9 '14 at 13:46