How many gallons does an inch of rain put off your roof?

The formula

One inch of rain on one square foot is 144 cubic inches, which is 0.623 of a gallon. So gallons = roof area (sq ft) × rain (in) × 0.623. Measure the roof's footprint from above, not the sloped surface: rain falls vertically, so a steep roof catches no more than a flat one of the same footprint.

Not all of it reaches the tank. Some splashes off, some wets the shingles and evaporates, and a first-flush diverter dumps the dirtiest first water of every storm. The site uses about 15% loss for asphalt shingles and 15 gallons of first flush per storm on a 1,500 sq ft roof.

Gallons per inch by roof size and material

Roof (sq ft)	metal	tile	asphalt	wood	gravel
1,000	592	561	530	499	468
1,500	888	842	795	748	701
2,000	1,184	1,122	1,060	997	935
2,500	1,481	1,403	1,325	1,247	1,169

Collection efficiency from the Texas Water Development Board's rainwater harvesting manual, which puts losses at roughly 10-25%; the per-material values sit within that range.

Why a barrel fills so fast

A 1,500 sq ft asphalt roof sheds about 795 gallons per inch, so a 55-gallon barrel is full after 0.07 of an inch once roof losses are counted, a light shower. Everything after that goes out the overflow, which is why the overflow should point away from the foundation. Across 3,206 cities that roof sheds a median 32,921 gallons a year, from 1,892 in Brawley, CA to 76,611 in Lincoln City, OR. How much of it is worth storing is a different question; see barrel or cistern.