Roof Slope Expressed as Rise-in-Run, Degrees, and Percentage
Roof Online Staff
Last updated July 10, 2020
The following table shows how the same common roof slopes can be expressed using rise-in-run ratios, degrees, and percentages.
See below, after the table, for directions on how to convert any roof slope from one form to another. Even roof slopes not shown in the table. It’s just a little math.
Also see our page, Quick Reference: Roof Slope: Degrees to Roof Pitch (Rise-in-Run) to see a table that gives the rise-in-run equivalents for roof slopes expressed in whole degrees from 1° to 72°.
If you’re not sure what the slope of your roof is and you want to determine that in either degrees or rise-in-run, we recommend this slope finder on Amazon.* It’s very inexpensive and very accurate.
If you’re using this table, you might like to get yourself a construction calculator. This one is very good.*
Rise-in-Run to Degrees: Find the arctangent of (rise/run).
(There’s a good calculator here. Click the “2nd” button in the top left of the calculator field to find the “atan” (arctangent) button. Enter the number (0.54167 in the following example) and click the “atan” button and then the “=” button.)
Example: For a 6-1/2 inch in 12 inch slope (6-1/2 = 6.5),
arctan(6.5 divided by 12)
arctan(0.54167) = 28.44° slope.
Rise-in-Run to Percentage: Divide the rise by the run and multiply by 100.
Example: For a 3/8 inch in 12 inch slope (3/8 = 0.375),
0.375 divided by 12 = 0.03125
0.03125 x 100 = 3.125
3/8 in 12 slope = 3.125% slope.
Degrees to Percentage: Find the tangent of the degree value. Multiply by 100.
Example: For a slope of 25°,
tan(25) = 0.4663
0.4663 x 100 = 46.63
25° slope = slope of 46.63%
Degrees to Rise-in-Run: Find the tangent of the degree value. Multiply the tangent by the run (which is 12, since we’re doing this in inches). That gives you the rise. Put them together as Rise-in-Run.
Example: For a slope of 35°,
tan(35) = 0.700
0.7 x 12 = 8.4
giving you a slope of 8.4-in-12 or
8-2/5 inches in 12.
Percentage to Degrees: Divide the percentage number by 100. Find the arctangent of the resulting value.
Example: For a slope of 55%,
55 divided by 100 = 0.55
arctan(0.55) = 28.81
55% slope is equal to a slope of 28.81°.
Percentage to Rise-in-Run: Divide the percentage number by 100. Multiply the result by the run (which is 12, since we’re doing this in inches). That gives you the rise. Put them together as Rise-in-Run.
Example: For a slope of 25%,
25 divided by 100 = 0.25
0.25 x 12 = 3
giving you a slope of 3-in-12.