The calculation I've always been given is that for every 1000 square feet of roof, 1" will provide 600 gallons. I've never checked the math on that, but based on my experience with a 240 square foot collection area and a 275 gallon IBC tote, it's in the ball park.
Yea, there seems to be no easy method to get this calculated. I'm reading about "collection effeciency" and so forth now. Honestly, it's not worth it other than it is sort of a fun puzzle to solve. "Ball park" is all I need. I may need to climb up on the roof and measure it now

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At your rate, that is .6 gallons per sq ft, per 1" of rain. So I got .4" of rain last night, that filled me to about 100 gallons.
.6 (gallons) x 672 (sq feet) x.4 (inches of rain last night)=161.28 gallons. So, given this equation my collection efficency is about 61%, that's if my #'s are right. I could have less sq feet and my rain gauge is the cheapest they make

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Another factor at play here....is my diverter capable of gathering 100% of the runoff? I don't think so, I think most of the water I'm losing is simply because the diverter can't keep up and the overflow is going into the downspout. The rest of my system should be big enough not to bottleneck the flow into the barrels.
But again, "ballparking" it is all i really need. And if I can fill it up every time it rains an inch, I'm a happy camper. We get on average about 4 inches of rain per month in the summer. That means I can, on average, drain the system once a week and expect it to refill.