# How to Convert Pitch Rate to Angle
A slope may be expressed as a ratio of the height gained over a set distance. For example, a roof that gains 9 inches in height over a horizontal distance of 12 inches has a pitch of 9:12. Sometimes it is useful to convert the ratio to an angle, particularly when determining the necessary angles at which to cut new roof supports. Converting from a ratio to an angle is a simple process, but a calculator is required.
Things You'll Need
- Scientific calculator
Instructions
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Divide the first number in the ratio by the second number. For example, the ratio 9:12 becomes 9/12 or 0.75. This value is the tangent, or Tan, of the roof angle.
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Enter the value of the tangent into a scientific calculator. Use the "Inv" and "Tan" functions, or the Arctangent function, to convert the tangent into an angle expressed in degrees. For example, if the tangent is 0.75, the inverse tangent is 36.87 degrees.
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Round the result to the nearest workable unit. This is usually the nearest degree. Instruments used to measure roof angles have limited accuracy and cannot normally measure fractions of a degree.
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