A useful reddit answer

mrCloggy said:

Just in case you are not familiar with electrical stuff:
Energy (Wh) = Power (Watt) x time (hour), needed for battery capacity.
Power (Watt) = Volt x Ampere, the momentary drain of the battery.
Example for a phone:
Phone battery is 3.7V, 2000mAh.
Energy storage is 3.7V x 2Ah = 7.4Wh.
Power needed to charge in 2 hours is 7.4Wh / 2 hr = 3.7W, to charge in 4 hours it would be 1.85 Watt.

If your computer uses 20 Watt, and is in use for 8 hours, you need 160 Wh to charge it again, 160 W in 1 hr, or 40W during 4hr.

You not only need the total Power (your 250W), but also the time it takes to charge them, to calculate the solar panel and big-storage battery.

To find out how much solar energy is available at your location, you can use http://pvwatts.nrel.gov/ (use the worst case nov/dec values) to get an idea of the panel size.
(It gives kWh/kWp per month, divide (by 31) and with your requirements in Wh/day to get the panel size).

You don’t want to drain your battery completely, (very short life span), and there may be some cloudy days you want to cover, the battery capacity (ideally) is > 4 x ‘daily Wh’.
Example:
Daily use is 700Wh, battery voltage is 12.5V, battery capacity is 4x 700Wh/12.5V=224Ah.
Assume 80% efficiency, choose the next bigger one.

The total ‘Power’ you use dictates the 12Vdc-to-120Vac(?) inverter size, you don’t want to run it at 100% (it gets too hot).
If 250W (at the same time) is your use, choose a >300W inverter.

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