Roof angles are commonly expressed in one of two ways: as an angle or as a ratio. When given as a ratio, the pitch takes the form "x : y," "or x / y," where "x" is the difference in height and "y" is the horizontal distance over which the height change occurs. For example, a pitch ratio of 9:12 means the roof gains 9 inches in height for every 12 inches of horizontal distance. Converting from an angle to a pitch ratio is straightforward. You will need a scientific calculator.

- Skill level:
- Moderately Easy

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### Things you need

- Scientific calculator

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## Instructions

- 1
Enter the value of the angle into the calculator. Use the "Tan" function to ascertain the tangent of the angle. For example, the tangent of 45 degrees is 1, and the tangent of 60 degrees is 1.732. Record this value.

- 2
Determine the horizontal distance, in inches, over which the roof pitch is to be measured. The pitch ratio is commonly given over 12 inches, but you may use any value.

- 3
Multiply the tangent of the angle you ascertained in Step 1 by the horizontal distance determined in Step 2. The result is the increase in height over the chosen distance.

#### Tips and warnings

- The tangent of an angle in a triangle is the length of the side opposite the angle divided by the length of the side adjacent to the angle. The opposite side is vertical, and the adjacent side is the horizontal base of the triangle.
- The pitch ratio is only as precise as the original angle measurement. Do not assume that the angle stated on the building plans is the same as the actual angle on the roof.
- If it is necessary to measure the roof angle "in situ," take all necessary safety measures appropriate to the height, condition and steepness of the roof. A fall may result in injury or death.

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#### References

- University of Georgia - College of Education; Mathematics in Construction; J. Wilson
- University of Maryland - Physics; Quiz9; Greg Jenkins; 2009
- Clark University - Department of Mathematics and Computer Science; Right Triangles; David E. Joyce
- Washington State Department of Labor & Industries: Roofer Falls From Roof After Un-clipping From Lifeline