calcs.homes
calcs.homes
Enter rise and run in any matching unit to get the angle in degrees, percent grade, and a simplified ratio — works for stairs, roof pitch, ramps, or any incline.
Rise and run must be in the same unit — the result is unit-independent.
We take the arctangent of rise divided by run, converted from radians to degrees, to get the angle from horizontal. Percent grade is that same rise-over-run ratio expressed as a percentage instead. For the ratio, we divide both rise and run by their greatest common divisor to reduce it to simplest whole-number form, like "4:12" or "1:3".
Percent grade and ratio notation are the same rise-over-run relationship written in whatever format each trade actually uses — carpenters call out roof pitch as a ratio with run fixed at 12 (like "4 in 12"), civil engineers and road signage rely on percent grade, and accessibility codes often specify a ratio or angle limit directly. Because percent grade is a straight ratio while degrees measure an actual angle, the two track together but aren't proportional — a 100% grade is a 45° angle, not 90° — so converting properly matters more than eyeballing one from the other.
Enter the pitch's rise (first number) and run (always 12 for standard roof pitch notation, like "4 in 12") — the angle in degrees appears as the primary result.
Percent grade is rise divided by run as a percentage — a straightforward ratio. Degrees measure the actual angle from horizontal. They track together but aren't proportional: a 100% grade is a 45° angle, not 90°.