How to Find the Roof Pitch From Angles

Updated February 21, 2017

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.

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.

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.

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.


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.

Things You'll Need

  • Scientific calculator
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About the Author

David Robinson has written professionally since 2000. He is a Fellow of the Royal Geographical Society and the Royal Meteorological Society. He has written for the "Telegraph" and "Guardian" newspapers in the U.K., government publications, websites, magazines and school textbooks. He holds an honors Bachelor of Arts in geography and education and a teaching certificate from Durham University, England.