That is a deep, dark rabbit hole Mr. Monkey.
Take the blue pill and stay in Neverland.... or take the red pill and see how deep the rabbit hole goes...
The short answer is that, yes, there are formulas and they do apply to the home and appliances. They are scary. Not because they are complex but because they usually mean you have to spend a lot of money to feed your energy habit via solar power. There are many reasons for this:
1) Our appliances are made so suck power with abandon because they are easy to make that way and our power is fairly cheap
2) Solar panels are expensive
3) Storing adequate power for when the sun is not shining is an additional huge expense.
But, to the point....
Watts = Amps X Volts.
We'll assume a 12 volt solar set up for simplicity's sake.
Say you have a 10 Amp Hour (AH) 12 volt battery. This is tiny and just used for example. Also for tiny example, let's way we have a "10 Watt" solar panel. (Enter the rabbit hole...) Now that doesn't mean you'll get 10 watts out of it. It is usually an 18v panel but the battery is going to pull that down to around 12v in actual use. So an 18v panel giving 10 watts is...
10 = 18 X ~.5555555
That is a .5 amp panel rounded down for lots of reasons. Its still probably a little high.
So... filling a 10AH battery with that 10 watt panel will take... 20 hours of max output conditions. In Hawaii that's from 10am to 3pm if you move the panel to catch the sun directly.... etc. In real life its more like 3 or 4 days of brilliant sun for that tiny panel to fill that tiny battery.
That 10AH battery would power a single 40 watt florescent bulb for.... back to our formula...
40 Watts = 12 volts X 3.333 amps. (Yes, I know. This assumes a 12v bulb and leaves out the 10% or so inefficiency of a DC/AC conversion)
3 hours. 10AH divided by 3.33 amp draw.
But (deeper we go...) If you draw a battery at more than 10% of its rate it is far less efficient. That will likely be more around 1.5 hours.
The solution is to get a MUCH bigger battery. If you want to run that light as efficiently as possible then you'll want a battery that is 10 times it's amp draw - we'll say a 35AH battery.
A 35 AH battery would take a week and a half to charge with that tiny panel and run the 40W light for.... 10 hours.
So... we need a larger panel. Say we use that light only for 3 hours a day. That's 10AH. So we need enough panel output to gather 10AH of power during the good light from 10 to 3 - a 5 hour window. Voila - we need 2 amps of panel (~30 watts, rounded up for safety) to:
1) Gather enough power to run that bulb for 3 hours a day
2) With a battery large enough to handle the load efficiently.
So that's a $70 battery and a $130 panel to run a single 40W light bulb for 3 hours a day. Add a charge controller for $25 and some other bits for an additional $50 or so.
The nice thing about that example is that you can probably run a laptop off that for about the same amount of time - if you don't use the light. For systems up to 500W or so you won't have to upgrade the charge controller, either.
As for appliances, a 500W system would probably ~run~ your fridge without any trouble but it will choke on compressor when it tries to kick in. The answer, of course, is yet more battery which would then seem to demand yet more solar panel, larger inverter, larger and more complex charge controller...
You see how this goes? Its actually cheaper in the long run to drop $1200 on a 40 watt solar fridge. Yes, a full size fridge/freezer that runs on 40 watts - same as the light bulb. Worth its price if you are trying to live off the grid.
That's the basic process, though. Small systems are relatively cheap, easy to set up and rewarding. Trying to seriously reduce your dependence on the grid requires either serious cash or a serious commitment to changing your energy habits, appliances and less (but still serious) cash.
A good resource for more information are folks who live in RV's. A lot of them use solar to help avoid having to run the engine to beef up the batteries. Here's a site that I found really helpful when I was digging through all this stuff a few years back:
http://www.marxrv.com/12volt/12volt.htmI chose to go the route of a small system - mostly cobbled together from cheap junk on ebay - that I can use to charge my laptop, tablet and AA batteries in addition to a couple marine batteries from WallyWorld. Then I favor devices that run on AA's or charge via USB. That gives me enough power for emergencies since I keep the marine batts topped off and small scale stuff to play around with - charging the cell phone and other gadgets. Fun, a good exercise - but nowhere near cost effective unless you value the self sufficiency enough to offset the costs.
Which is the niche that Goal Zero is filling pretty darned well.