Roof Pitch Calculator Formula

Understand the math behind the roof pitch calculator. Each variable explained with a worked example.

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Formulas Used

Pitch (X/12)

pitch_notation = rise * 12 / run

Angle (Degrees)

angle_degrees = (180 / 3.14159) * (rise / run > 0 ? (rise / run - pow(rise / run, 3) / 3 + pow(rise / run, 5) / 5) : 0)

Pitch Factor (Multiplier)

pitch_factor = sqrt(1 + pow(rise / run, 2))

Slope (%)

slope_percent = rise / run * 100

Variables

VariableDescriptionDefault
riseRise(inches)6
runRun(inches)12
slope_ratioDerived value= rise / runcalculated

How It Works

How to Calculate Roof Pitch

Formula

Pitch = Rise / Run (typically expressed as X:12)

Angle = arctan(Rise / Run) in degrees

Pitch Factor = sqrt(1 + (Rise/Run)²)

Roof pitch is expressed as the number of inches of rise per 12 inches of horizontal run. For example, a 6/12 pitch rises 6 inches for every 12 inches of run. The pitch factor is used to convert footprint area to actual roof area.

Worked Example

A roof with 6 inches of rise per 12 inches of run (6/12 pitch).

rise = 6run = 12
  1. 01Pitch = 6/12
  2. 02Angle = arctan(6/12) = arctan(0.5) = 26.6 degrees
  3. 03Pitch factor = sqrt(1 + 0.5²) = sqrt(1.25) = 1.1180
  4. 04Slope = 0.5 × 100 = 50%

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