The following table shows how common roof slopes are expressed in their rise/run ratio, degree, and percentage equivalents.

(See below, after the table, for how to convert any slope. Even roof slopes not shown in the table. It’s just a little math.)

Roof Slope
(Rise Over Run)
Roof Slope
(Degrees)
Roof Slope
(Percentage)
0.25/12 1.193° 2.083 %
0.5/12 2.386° 4.167 %
1/12 4.76° 8.333 %
2/12 9.46° 16.667 %
3/12 14.04° 25.000 %
4/12 18.43° 33.333 %
5/12 22.62° 41.667 %
6/12 26.57° 50.000 %
7/12 30.26° 58.333 %
8/12 33.69° 66.667 %
9/12 36.87° 75.000 %
10/12 39.81° 83.333 %
11/12 42.51° 91.667 %
12/12 45° 100.000 %
13/12 47.29° 108.333 %
14/12 49.4° 116.667 %
15/12 51.34° 125.000 %
16/12 53.13° 133.333 %
17/12 54.78° 141.667 %
18/12 56.31° 150.000 %
19/12 57.72° 158.333 %
20/12 59.04° 166.667 %
21/12 60.26° 175.000 %
22/12 61.39° 183.333 %
23/12 62.45° 191.667 %
24/12 63.43° 200.000 %
25/12 64.36° 208.333 %
26/12 65.22° 216.667 %
27/12 66.04° 225.000 %
28/12 66.80° 233.333 %
29/12 67.52° 241.667 %
30/12 68.20° 250.000 %
• Rise over 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 example) and hit 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 over 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 over 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/Run.

Example: For a slope of 35°,

tan(35) = 0.700

0.7 x 12 = 8.4

giving you a slope of 8.4/12 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 over 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/Run.

Example: For a slope of 25%,

25 divided by 100 = 0.25

0.25 x 12 = 3

giving you a slope of 3/12.