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. The roof pitch multiplier is determined by finding the square root of ((rise/run)² + 1). The slope of the roof provides the rise and the run to be plugged into the equation. A roof pitch of 4/12 has a rise of 4 and a run of 12.

If you know the roof pitch in degrees, find the secant 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/Run, Degrees, Percentage.)

The roof pitch factor is also used to calculate the length of common rafters. In this case, the multiplier is multiplied by the run of the rafter (the horizontal distance that will be covered by the rafter). For precision, the thickness of the ridge board and any eave overhang should also be taken into account when determining the correct length of the rafters.

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

(Always measure for every rafter, ¼-inch makes a difference.)

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

Roof Pitch (In Degrees) Roof Pitch Multiplier
1/12 4.76° 1.003
2/12 9.46° 1.014
3/12 14.04° 1.031
4/12 18.43° 1.054
5/12 22.62° 1.083
6/12 26.57° 1.118
7/12 30.26° 1.158
8/12 33.69° 1.202
9/12 36.87° 1.250
10/12 39.81° 1.302
11/12 42.51° 1.357
12/12 45° 1.414
13/12 47.29° 1.474
14/12 49.4° 1.537
15/12 51.34° 1.601
16/12 53.13° 1.667
17/12 54.78° 1.734
18/12 56.31° 1.803
19/12 57.72° 1.873
20/12 59.04° 1.944
21/12 60.26° 2.016
22/12 61.39° 2.088
23/12 62.45° 2.162
24/12 63.43° 2.236
25/12 64.36° 2.311
26/12 65.22° 2.386
27/12 66.04° 2.462
28/12 66.80° 2.539
29/12 67.52° 2.615
30/12 68.20° 2.693