How to Calculate Roof Pitch: Rise Over Run, Degrees and a Pitch Chart

Roof pitch is the rise in inches for every 12 inches of horizontal run: pitch = rise ÷ run × 12. A roof that rises 6 inches over 12 inches of run is a 6/12 pitch, which is 26.57 degrees or a 50% slope.

To get the angle from any rise and run, take arctan(rise ÷ run). Stairs use the same rise and run geometry, with the stair angle taken from riser and tread: see the Stair Calculator.

What is roof pitch?

Roof pitch is the steepness of a roof, written as how many inches it rises for every 12 inches it runs horizontally. A “6/12 pitch” (also written 6:12) rises 6 inches over 12 inches of level run. Slope is the same steepness written another way: as an angle in degrees or as a percent. Run is always the level distance, not the distance along the rafter.

The formula

pitch (rise per 12 in) = rise ÷ run × 12
angle (degrees)        = arctan(rise ÷ run)
percent slope          = rise ÷ run × 100
rise                   = pitch ÷ 12 × run

Rise and run must use the same unit. 4 ft of rise over 12 ft of run is a 4/12 pitch, just as 4 in over 12 in is. The roof area factor, √(1 + (rise ÷ run)²), turns a flat footprint into a sloped roof area. How to use it is covered in how to calculate roof square footage.

How to measure roof pitch

From the attic

Hold a level horizontal against the underside of a rafter and mark 12 inches along it. Measure straight up from that mark to the rafter. The number of inches is the rise, so a reading of 5 inches means a 5/12 pitch. This keeps you off the roof.

From the ground or from plans

On a simple gable roof, the run is half of the building width, measured between the outside faces of the walls. The rise is the height from the top of the wall to the ridge. A laser distance measurer or the elevation drawing gives both. Then pitch = rise ÷ run × 12.

From an angle reading

If an angle finder or a phone inclinometer reads degrees, convert with pitch = tan(angle) × 12. Use the table below instead of the formula if you prefer.

Roof pitch chart

Each row below is computed from the formulas above. The area factor is the number to multiply a flat footprint by to get roof area.

Degrees to pitch

Percent slope is not the same as degrees. A 100% slope is 45°, not 100°.

Worked examples

Example 1: from the attic. The level is held flat, and the rafter is 5 inches above the 12-inch mark.

• Pitch: 5 ÷ 12 × 12 = 5, so 5/12
• Angle: arctan(5 ÷ 12) = 22.62°
• Percent slope: 5 ÷ 12 × 100 = 41.7%
• Area factor: √(1 + (5 ÷ 12)²) = 1.0833

Example 2: from a gable end. The building is 28 ft wide, and the ridge is 7 ft above the top of the walls.

• Run: 28 ÷ 2 = 14 ft
• Pitch: 7 ÷ 14 × 12 = 6, so 6/12
• Slope length of one side: 14 × 1.1180 = 15.65 ft. This is the length along the slope for the run, and it is not a rafter cut length because it ignores overhangs, the ridge and the bearing cuts.

Example 3: from an angle. An angle finder reads 30°.

• tan(30°) = 0.5774
• Pitch: 0.5774 × 12 = 6.93, so about 6.93/12
• Area factor: √(1 + 0.5774²) = 1.1547

Example 4: finding the rise. You want a 4/12 pitch over a 10 ft run.

• Rise: 4 ÷ 12 × 10 = 3.3333 ft, which is 3 ft 4 in

What about low-slope roofs?

Whether a roofing material works on a given pitch is set by the manufacturer and the local building code, not by the math. For asphalt shingles, the Asphalt Roofing Manufacturers Association says never to apply shingles on roofs with slopes lower than 2 inches per foot (2:12). For slopes from 2:12 to less than 4:12, it describes special underlayment methods: either a double layer of felt or synthetic underlayment, or a single layer of self-adhering underlayment. A city building department’s summary of the International Residential Code, section R905.2, says the same: asphalt shingles on slopes of 2:12 or greater, with double underlayment from 2:12 to 4:12.

• Code editions and local amendments differ, so confirm what your jurisdiction has adopted.
• Manufacturer installation instructions can be stricter than the code, and installing outside them can affect a warranty.
• Other roofing materials, such as metal, tile, membranes and wood shakes, have their own minimum slopes. Read the maker’s instructions for the product you plan to use.

Assumptions and safety

• This guide is geometry. It converts between forms of the same slope and does not design rafters, trusses, sheathing or fasteners.
• Snow, wind and seismic loads depend on your location and the framing. A pitch alone does not tell you whether a roof is adequate, so ask your local building department or an engineer.
• Real roofs are not perfectly flat or square. Measure more than one place on a plane that looks uneven.

Questions people ask