Is there a formula that can calculate rainfall on a gallons-per-square-mile basis?

It’s a relatively straightforward conversion problem. Once you figure out how big the drops are (and if you have a good count of “drops per minute” per area) then it’s not hard at all.

The tough parts, as I see them, are evaluating the area that receives 7200 drops per minute (per square foot? per inch? what small area is receiving that level of rainfall?), and then being certain of the total area covered. For example, with a thunderstorm, it’s pretty unlikely that the entire county received the same rate of rainfall for the same period, since T-storms are more localized and they travel.

In any case, the measure you’re after is “acre-feet”, and it’s a common unit of measure when you’re dealing with large areas of water coverage (mostly ponds and lakes, but your example is close enough to that).

EDIT: 1 Acre-Foot of water is 325,852 US gallons.

I wanted to add that the other tough part is going to be evaluating an average “drop size”.

What’s wrong with using the rain gauge and simply extrapolating over the area you want to describe?

1 inch of rain over a square mile means, that on average, a square mile is flooded with water to the depth of 1 inch. If you convert the volume of 1” x 1 mile x 1 mile into gallons, you will get the conversion of 1” rain => x gallons water.

1 inch of rain over a square mile is 4014489600. cubic inches. Ther are 231 cubic inches per gallons so.
1 inch of rain per square mile is 17,378,742 gallons.

All of you, thanks enormously for the help. This is exactly the info I was looking for.

(Of course, the trick is measuring the “velocity” of the rain, and whether it is consistent all over the square mile, but that’s another issue.

My calculations are in rough agreement with @LuckyGuy:

1 acre-foot of water = 325,852 gallons (as noted above – and that was a rounded number)
* 640 acres in a square mile = 208,545,280 gallons per square mile – foot
÷ 12 = 17,378,773 gallons per square mile – inch

At that kind of scale, no one is going to notice a difference of 31 gallons, obviously. (You’ll lose much more than that in the first day’s evaporation, as soon as the rain stops.)

@CWOTUS Glad to see we agree.
My number is exact by the way. No rounding was necessary.

Hmm. Well, it’s true that you did no rounding, but when you divided the total cubic inches in a square mile – inch (and what an odd measure that is) by 231 you got a decimal remainder that you wrote off (and who wouldn’t?). (The rounding that I did was in cutting off the decimals in gallons of water per acre-foot, again because “who cares?”)

But that’s the point I’m trying to make. There’s no way to accurately measure the amount of rain that is occurring or has occurred over a given square mile (since rainfall itself is so variable over time and area during any storm event) or to precisely measure the accumulation once it has occurred, and back-figure from that what the rate per time and per area was.

So it hardly matters how precisely we can calculate how much water a given volume is to the cubic inch; at this level of event all of our numbers are going to be rough approximations anyway.