Roof Pitch Calculator

Roof Pitch formula

Pitch = Rise / Run x 12  (written as x/12)
Angle (degrees) = atan(Rise / Run)
Slope % = Rise / Run x 100
Pitch factor = sqrt(1 + (Rise / Run)^2)

Worked example

A ridge 5 ft above the top of the walls on a 30 ft wide building: run = 30 / 2 = 15 ft, and rise / run = 5 / 15 = 0.333. The pitch is 0.333 x 12 = 4/12. The angle is atan(0.333) = 18.4 degrees, the slope is 33.3%, and the pitch factor is sqrt(1 + 0.333²) = 1.054. Every foot of run needs 12 x 1.054 = 12.65 in of rafter.

Measured with a level on the roof: a 9 in drop over 12 in is a 9/12 pitch, which is 36.9 degrees, a 75% slope and a factor of 1.25. A house with a 30 x 40 ft roof footprint at 9/12 has 1,200 x 1.25 = 1,500 sq ft of roof surface.

Quick reference

How to measure roof pitch

From the roof or a ladder, hold a level horizontally with one end touching the shingles. Mark 12 inches from that end, then measure straight down from the mark to the roof surface. That distance in inches is the pitch over 12. A 6 inch drop is a 6/12 pitch. Doing this on the underside of a rafter in the attic gives the same answer without climbing on the roof.

If you can only measure from the ground, use total rise and span. Measure the building width, and estimate the ridge height above the top of the walls from a photo or by counting siding courses. Half the width is the run, and rise divided by run times 12 is the pitch. On a hip roof the run is still half the width of the building for the main slopes.

Angle, slope and pitch factor

Pitch, angle and slope percent are three ways of describing the same steepness. Roofers use x/12, engineers and saw settings use degrees, and site plans sometimes use percent. Convert pitch to degrees with the arctangent of rise over run: atan(6 / 12) = 26.6 degrees.

The pitch factor is what you multiply the flat footprint area by to get the actual roof surface area. At 6/12 the factor is 1.118, so a 1,000 sq ft footprint has 1,118 sq ft of roof. The same factor gives rafter length per foot of run, which is how rafter tables on a framing square are built.

Key facts

• A 12/12 pitch is a 45 degree roof. A 6/12 pitch is 26.6 degrees, not half of 45.
• Pitch factors: 4/12 = 1.054, 6/12 = 1.118, 8/12 = 1.202, 10/12 = 1.302, 12/12 = 1.414.
• The IRC allows asphalt shingles down to a 2/12 pitch, and pitches from 2/12 to 4/12 require two layers of underlayment.
• Most houses have roofs between 4/12 and 9/12. Pitches of 6/12 and under are generally walkable; steeper roofs need roof jacks or scaffolding.
• A 6/12 pitch is the same as a 1:2 ratio or a 50% grade, both of which appear on architectural drawings.

Frequently asked questions

Sources and references

• •Chapter 9 Roof Assemblies, 2021 IRC (ICC)
• •Asphalt Roofing Residential Manual: Design and Application Methods (Asphalt Roofing Manufacturers Association)
• •Application of Asphalt Shingles on Slopes Greater than 21:12 technical bulletin (Asphalt Roofing Manufacturers Association)