How to calculate a roof angle for construction

Written by grant d. mckenzie
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How to calculate a roof angle for construction
The angle of the roof is the arctangent of the rise over the run from your measurements. (Getty Images)

The roof angle, which is also called the roof pitch, is an important value in roof construction. The roof pitch/angle will dictate what materials should be used to cover the roof and what environmental conditions the roof can withstand. For instance, a roof in a snowy climate will need a steeper pitch than one in a temperate climate so it will not collapse under the weight of accumulated snow. Determining the pitch of an existing roof is an easy and straightforward process.

Skill level:

Things you need

  • Ladder
  • Level (at least 30 cm - 1 foot - in length)
  • Ruler or tape measure
  • Calculator (optional)

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  1. 1

    Set the ladder in an area that allows clear access to the roof and climb to the roof level with the level and ruler or tape measure.

  2. 2

    Mark off 30 cm (1 foot) on the level. It is better to have a level that also has a measurement scale, but it is not necessary.

  3. 3

    Lay the level on the roof and raise the lower end until the indicator is centred, meaning the level is horizontal.

  4. 4

    Use the ruler to measure from the 30 cm (1-foot) mark on the level to the roof surface. Keep the ruler or tape measure perpendicular to the level. The pitch is indicated by this measurement. For example, if the perpendicular distance from the level to the roof surface is 10 cm (4 inches), the pitch would be written as "10:30" (or equivalently 1:3), meaning 10 cm of rise per 30 cm of run (in imperial this would be "4:12," or four inches of rise per 12 inches of run).

  5. 5

    Divide the rise by the run and calculate the inverse tangent, or arctangent, of the result to determine the angle. For the "10:30" example, the calculation would be: 10/30 = 0.333 atan(0.333) = 18.4 degrees

Tips and warnings

  • The angle calculation is rarely needed because most suppliers and contractors use the "rise:run" format.

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