A roof pitch multiplier, also called a roof pitch factor, is a number that is multiplied by the area covered by a sloped roof to produce the area of the actual surface of the roof. For roof slopes expressed as “X-in-12” (rise-in-run), the roof pitch multiplier is determined by finding the square root of ((rise/run)² + 1).

Divide the rise by the run (the run is 12). Square the result. Add 1. Find the square root of the result.

The slope of the roof provides the rise and the run to be plugged into the equation. A roof pitch of 4-in-12 (4:12) has a rise of 4 and a run of 12.

The roof pitch factor is also used to calculate the length of common rafters. To find the total length of a common rafter, consider the run to be the horizontal distance covered by the whole rafter, from the end of the rafter tail (the part of the rafter which extends past the outside of the wall) to the near side of the ridge board.

To find the location of the heel cut, the multiplier is multiplied by the “effective run” of the rafter. The effective run is the horizontal distance covered by the rafter from the near side of the ridge board, where the head cut will be, to the outside of the wall plate, where the heel cut will be.

Always measure for every rafter, even being off ⅛-inch can make a big difference if the error gets multiplied as you go along.

 
An accurate measurement of the slope is one of the most important pieces of information to have about a roof.

An accurate measurement of the slope is one of the most important pieces of information to have about a roof.

 

The following table provides the roof pitch multiplier for roofs of various slopes. For a more detailed explanation of the roof pitch multiplier, see "How to Find the Area of a Sloped Roof".

If you know the roof pitch in degrees, find the secant of the slope using a scientific calculator. For example, if the roof pitch is 45°, then sec(45) = 1.414213. That's your roof pitch multiplier.

For help converting any slope from one way of expressing it to another, see Roof Slope Expressed as Rise-in-Run, Degrees, and Percentage.

If you’re not sure what the pitch of your roof is and you want to figure that out, we recommend this slope finder on Amazon.* It’s very inexpensive and very accurate.

One more thing: if you’re using this table, you should consider getting yourself a construction calculator. This one is very good.*

Roof Pitch Multiplier Table
Roof Slope
(Rise-in-Run)		 Roof Slope
(In Degrees)		 Roof Pitch Multiplier
0.5-in-12 2.39° 1.001
1-in-12 4.76° 1.003
1.5-in-12 7.13° 1.008
2-in-12 9.46° 1.014
2.5-in-12 11.77° 1.021
3-in-12 14.04° 1.031
3.5-in-12 16.26° 1.042
4-in-12 18.43° 1.054
4.5-in-12 20.56° 1.068
5-in-12 22.62° 1.083
5.5-in-12 24.62° 1.100
6-in-12 26.57° 1.118
6.5-in-12 28.44° 1.137
7-in-12 30.26° 1.158
7.5-in-12 32.01° 1.179
8-in-12 33.69° 1.202
8.5-in-12 35.31° 1.225
9-in-12 36.87° 1.250
9.5-in-12 38.37° 1.275
10-in-12 39.81° 1.302
10.5-in-12 41.19° 1.329
11-in-12 42.51° 1.357
11.5-in-12 43.78° 1.385
12-in-12 45° 1.414
12.5-in-12 46.17° 1.444
13-in-12 47.29° 1.474
13.5-in-12 48.37° 1.505
14-in-12 49.4° 1.537
14.5-in-12 50.39° 1.568
15-in-12 51.34° 1.601
15.5-in-12 52.25° 1.634
16-in-12 53.13° 1.667
16.5-in-12 53.97° 1.700
17-in-12 54.78° 1.734
17.5-in-12 55.56° 1.768
18-in-12 56.31° 1.803
18.5-in-12 57.03° 1.838
19-in-12 57.72° 1.873
19.5-in-12 58.39° 1.908
20-in-12 59.04° 1.944
20.5-in-12 59.66° 1.979
21-in-12 60.26° 2.016
21.5-in-12 60.83° 2.052
22-in-12 61.39° 2.088
22.5-in-12 61.93° 2.125
23-in-12 62.45° 2.162
23.5-in-12 62.95° 2.199
24-in-12 63.43° 2.236
24.5-in-12 63.90° 2.273
25-in-12 64.36° 2.311
25.5-in-12 64.80° 2.349
26-in-12 65.22° 2.386
26.5-in-12 65.64° 2.424
27-in-12 66.04° 2.462
27.5-in-12 66.43° 2.500
28-in-12 66.80° 2.539
28.5-in-12 67.17° 2.577
29-in-12 67.52° 2.615
29.5-in-12 67.86° 2.654
30-in-12 68.20° 2.693
30.5-in-12 68.52° 2.731