Roof Pitch to Slope Angle

Roofers do not talk in degrees, they talk in twelfths. A "4:12" roof rises 4 inches for every 12 inches of level run, and the number 12 is baked into the framing square, the rafter tables, and the shingle warranty. Converting to an angle is just $\theta = \arctan(p/12)$, so 4:12 is 18.43°, 6:12 is 26.57°, and 12:12 is exactly 45°.

The angle version earns its keep when a tool needs it. Mitre saws, digital angle finders, solar array mounts and structural software all speak degrees, while the drawings speak twelfths. It is also the fastest way to check a manufacturer's limits: most asphalt shingles need a minimum 2:12 (9.46°) with a doubled underlayment, and 4:12 for standard application. Above about 6:12 you are into roof jacks and harnesses rather than walking the deck.

One trap: "pitch" in the strict old sense meant rise over the full span, so a roof with a 6 ft rise on a 24 ft span was "quarter pitch". Almost nobody uses that today, and this calculator uses rise per 12 of run, which is what the framing square measures.