How to Figure Out the Width With the Height and Slope of a Roof

Understanding a construction project mathematically or on paper before you begin the work of cutting and nailing reduces frustrations and construction time by ensuring an efficient and smooth process. When determining materials and labor required for a roof project, for example, get a handle on the dimensions you will be working with. Determining the width of a roof from the known values of height and slope can be done simply by using a step-by-step mathematical process.

Calculator

Instructions

Gather and Arrange Known Values
- 1
  
  Diagram the problem before you begin the calculations.
  
  Draw a simple sketch of the roof profile, represented as a triangle.
- 2
  Draw a vertical line from the roof peek to the midpoint between the eaves. Label this line "Height" and note its known dimension.
- 3
  Write the slope along the roofline. This value is a fraction with the rise over the run. A 10/12 slope, for example, has a rise of 10 units to a run of 12 units.
Calculate the Width
- 4
  
  Use a claculator to find the width.
  
  Multiply the known height by the run. For example, if the known slope is 10/12, the run is 12, and if the known height is 7 feet, multiply 7 and 12 equaling 84.
- 5
  Divide the product of the height and the run by the rise. If the slope is 10/12, the rise is 10 -- 84 divided by 10 equals 8.4. This number represents half the width of the roof.
- 6
  
  A combination of multiplication and division determines your final roof width.
  
  Multiply the last value by two. In the example, you would multiply 8.4 and two, resulting in a product of 16.8 feet. This is the full width of the roof.

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How to Figure Out the Width With the Height and Slope of a Roof

Instructions

Gather and Arrange Known Values

Calculate the Width