Pitch to Slope and Angle

The Pitch to Slope and Angle calculator returns the slope and angle based on a chosen pitch. 

INSTRUCTIONS: Enter the following:

• (P) Pitch Angle (rise over run)
  • Choose from List: flat, 1/12, 2/12, 3/12, 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 10/12, 12/12, 14/12, 16/12, 18/12, 20/12, 22/12, 24/12

Slope (m) and Angle (Θ): The calculator returns the slope as a real number and the angle in degrees. 

The Math / Science

The formula for the angle based on the pitch is:

      Θ = atan( rise / run)

where

• Θ = angle
• rise = vertical measurement
• run = horizontal measurement

The slope of an angle is a measure of its steepness or inclination. In geometry, the slope of an angle is typically defined as the ratio of the rise (vertical change) to the run (horizontal change) along the angle. It indicates how much the angle rises or falls for each unit of horizontal distance traveled.

In roofing geometry, slope represents the ratio of the vertical change to the horizontal change between any two points on the roof along the line heading directly to the ridge. This slope is also known as the gradient and can be calculated using the formula:

m = rise / run​

where:

• m = slope
• rise = vertical height
• run = horizontal length

Roofing Geometries Calculators

• Pitch to Slope: This converts pitch (e.g., 4/12) to slope.
• Pitch to Angle: This converts pitch (e.g., 10/12) to an angle in degrees.
• Rise over Run to Angle: This converts rise over run to an angle in degrees.
• Gambrel Angle: Computes the bend at the intersection of two slope as in a gambrel roof.
• Interface Angle: This computes the interface angle between two sloped surfaces.
• Interface Angle from Rise over Run: This computes the interface angle based on two rises and runs.
• Trusses Needed for a Roof: This computes the number of trusses needed for a roof based on the ridge length and truss spacing
• Roof Section Area: This computes the surface area of an irregular shaped section of a roof.
• Gable Roof Geometries: This computes the lengths and measurements for a gabled roof based on the ridge length, pitch, span and overhang.
• Dormer Geometries: This computes the measurements for a gable dormer based on the dimension of the dormer and main roof..
• Hip Roof Geometries: This the metrics associated with a hip roof based on the dimensions.
• Double Hip Roof Geometries: This compute the lengths of the dimensional lines where one hip roof intersects another such as in a dormer.
• Pyramid Hip Roof Geometries: This computes the lengths and dimensional lines of a pyramid roof.
• Gambrel Pitch Angles: This computes the pitch angles and rafter lengths in a gambrel roof bases on the span, total height, and height and width of the loft.
• Gambrel Rafter Lengths. This computes the upper and lower rafter lengths, attic width and total height under a gambrel roof based on the upper and lower pitch, span and loft height.
• Rafter Length: This computes the length of the rafters based on the span, pitch and overhang.
• Corrugation Factor: This computes the material length associated with a structural length using corrugated material.