How to Convert Roof Pitch to Degrees
(A table for quick reference is provided at the bottom of the page.)
To convert any roof pitch to its equivalent in degrees, you first need to make sure you understand what you mean by “roof pitch”. “Roof pitch” and “roof slope” are frequently used as if they mean the same thing, but they don’t.
Strictly speaking, roof pitch is the ratio of the height of the roof (from the level of the top of the exterior walls to the level of the ridge) to the width of the roof (from the outside of one exterior wall to the outside of the exterior wall across the building). Because “roof pitch” generally describes the total height and width of two sides of a roof which can, in some cases, have different slopes, it doesn’t quite make sense to talk about a roof pitch in degrees. What you are actually talking about in this case is roof slope, which refers to the number of inches the roof rises per 12 inches of run.
To convert a roof slope expressed as “X-in-12” to a roof slope expressed in degrees, find the arctangent of (rise/run).
There’s a good calculator here. Click the “2nd” button (top left of the calculator field). The “atan” (arctangent) button is the second from the bottom on the left side of the calculator field. First enter the number you got from dividing your rise by your run (0.791667 in the following example) Then click the “atan” button, and then the “=” button. This will give you the arctangent of (rise/run).
For a slope of 9½-in-12
Convert 9½ to 9.5
Divide 9.5 by 12 (rise/run is 9.5/12) to get 0.791667
Find the arctangent of 0.791667
Arctan(0.791667) = 38.367497125297
Round this to a reasonable number of digits. Let’s call it 38.37.
A 9½-in-12 roof slope is the same as a 38.37 degree slope.