Calculating the roof slope factor is not that difficult. All you need is a simple trigonometry equation and a calculator that has a square root button. If you need to find out the area of the roof, such as to purchase roofing, knowing and using the factor will assist you greatly in determining the exact square footage. Trigonometry is used because roof lines are really triangles; specifically, the roof is the hypotenuse, or the longest side, of a triangle.
Theory and Solution of Factor
The overall length of the roof or a common rafter, from the base to the ridge, is calculated by squaring the run, adding it to the square of the rise, and finding the square root of the sum. The result is divided by 12. Suppose you have a 6/12 pitch roof. Six squared is 36 and 12 squared is 144. Adding 36 plus 144 equals 180. The square root of 180 is 13.416. Dividing 13.416 by 12 equals 1.118. Therefore, your slope factor for a 6/12 pitch roof is 1.118.
You could calculate the slope factor for every single roof pitch, but as a public service, many roofing companies provide slope factor charts. For instance, the Ever Last Roofing company distributes a chart to the general public. Charts list the slope factor for various pitches, usually from 1/12 to 12/12.
Using the Factor
You don't have to climb a ladder and place a tape measure on the ridge, and measure down to the base to find the length of the roof. Use the factor instead. Measure from an exterior wall to an exterior wall and divide by two. Multiply the result by the factor, and this is the length of the roof from base to ridge. For example, suppose you have a 4/12 pitch roof, and the width of the house is 28 feet. Looking at the chart, the factor is 1.0541. Dividing the house width by two equals 14 feet. Multiply 14 by 1.0541, resulting in 14.75 feet. The length of the roof is 14 feet and three quarters of a foot, or 14 feet 9 inches.
Hip and Valley Rafters Slope Factor
Roofs with hips and valleys have special factors. A hip or a valley is where two roof slopes intersect, forming a peak or a depression. Charts are helpful because the factors for hips and valleys are listed, which is useful for cutting rafters on the hip or valley. For example, a shed has a 3/12 pitch roof with a outside wall dimension of 10 feet. Reading the chart, the factor for 3/12 is 1.4362. Half of 10 is five. Five times 1.4362 equals 7.18 feet, or 7 feet 2 inches.