ConstructionCalc

Roof Pitch Calculator: Degrees, Slope & Roof Height

Turn a measured rise and run, an angle, or a building’s width into the pitch, its angle and slope, the ridge height, and the roofing the 2021 IRC allows at that pitch.

By Marko VisicBSc Physics, University of Ljubljana

6/12

rise per 12 of run

26.6°, a 50% slope

12626.6°
Slope
50%
Rise per foot of run
6 in
Slope length over your run
13.42 in
Pitch multiplier
1.118
Whole pitch nearest
6/12
OSHA roof class
Steep

What the 2021 IRC allows at 6/12

Asphalt shingles
Allowed
Metal panels, standing seam
Allowed
Metal panels, lapped seams without sealant
Allowed
Clay or concrete tile
Allowed
Slate
Allowed
Wood shingles
Allowed
Mineral-surfaced roll roofing
Allowed

Over 4/12, OSHA counts a roof as steep: anyone working 6 ft or more above a lower level needs guardrails with toeboards, a safety net or a personal fall arrest system.

Find
Units

Hold a level flat against the roof, measure 12 inches along it and read the rise below, or enter a whole roof’s rise and run.

Pitch 6/12, 26.6°, 50% slope

Roof pitch is the rise for every 12 inches of level run. A roof that climbs 6 inches in 12 is a 6/12 pitch: 26.6 degrees and a 50% slope, and each foot of run takes 1.118 feet of roofing. A 30-foot-wide gable at that pitch rises 7.5 feet to its ridge.

Pitch decides which roofing the code allows, how much more roof there is than floor under it, and whether a crew needs fall protection. Start from whatever you can measure: a rise under a level, an angle from a phone app, or a building’s width and the pitch on its plans.

Code minimums come from the 2021 International Residential Code, Section R905; your local code and the roofing maker’s instructions can ask for more. How we check every figure: methodology.

How to measure your roof’s pitch

You need one rise and one run in the same unit. The quickest reading uses a level: on the roof or in the attic, hold it against the roofing or the underside of a rafter until the bubble is centered, mark 12 inches along it, and measure straight from that mark to the roof. That measurement is the pitch: a reading of 6 inches means 6/12.

From the ground, use the building instead. Measure its width between the outside faces of the walls and the ridge’s height above the wall tops. A gable roof slopes up from both walls, so its run is half the width; a shed roof slopes across the whole width. Enter that rise and run in any one unit. With an angle from an inclinometer or a phone app, use the angle mode.

Example: a level against a rafter reads 7.5 inches at the 12-inch mark. That is a 7.5/12 pitch, 32.0 degrees and a 62.5% slope, and every foot of run is 1.179 feet along the roof.

From pitch to degrees, slope and multiplier

Every figure the calculator shows comes from the rise per 12 of run. The angle and the slope describe the same tilt in other units; the multiplier is the one roofers reach for, because it turns level measurements into lengths and areas along the roof.

Angle in degrees = arctan(rise ÷ 12)

Slope in percent = rise ÷ 12 × 100

Pitch multiplier = √(1 + (rise ÷ 12)²)

At 6/12 the multiplier is 1.118, so a 20-foot run is 22.36 feet of rafter and a 1,000-square-foot plan is about 1,118 square feet of roof. At 12/12 the roof stands at 45 degrees and the multiplier is √2, or 1.414: there is about 41% more roof than floor.

The roof pitch chart lists all three figures for every pitch from 1/12 to 24/12, and converts degrees back to pitch.

Roof height and rafter length

A whole roof rises its run times the pitch over 12, and its rafter runs the run times the multiplier. The roof height mode does both, from the building’s width and the pitch.

Ridge height = run × pitch ÷ 12

Rafter, wall to ridge = run × pitch multiplier

Example: a 28-foot-wide garage with a 4/12 gable has a 14-foot run on each side. Its ridge sits 4.67 feet (4 ft 8 in) above the wall tops, and each rafter is 14.76 feet from the wall line to the ridge, or 15.81 feet with a 12-inch overhang.

That rafter length runs along the underside of the rafter, from the outside of the wall to the center of the ridge. The board you cut also depends on the ridge board’s thickness and the seat cut, so use it as the starting length rather than the cut length.

Why 4/12 is the line that matters

Three rules meet at 4/12. OSHA calls a roof of 4/12 or less a low-slope roof and anything over 4/12 a steep roof. On a steep roof, anyone working 6 feet or more above a lower level has to be protected by guardrails with toeboards, a safety net or a personal fall arrest system.

The 2021 IRC uses the same line for underlayment. Asphalt shingles need double underlayment from 2/12 up to 4/12, clay and concrete tile from 2½/12 to 4/12, and slate starts at 4/12. Below the shingle range, standing-seam metal panels go down to ¼/12, and membranes such as modified bitumen start at ¼/12. The calculator checks your pitch against these minimums and lists what is allowed under the answer; the guide to the minimum roof pitch for shingles and every other roofing sets them all out.

Roof pitch calculator FAQ

How do I convert roof pitch to degrees?

Divide the rise by 12 and take the arctangent. A 6/12 pitch is arctan(0.5), or 26.6 degrees, and a 12/12 pitch is 45 degrees. To go the other way, multiply the tangent of the angle by 12: a 30-degree roof is a 6.93/12 pitch.

What is a roof pitch multiplier?

It is the length along the roof for each unit of level run: the square root of 1 plus the square of the rise over 12. Multiply a run by it for the slope length, or a footprint by it for the roof area. A 6/12 roof’s multiplier is 1.118.

How do I measure roof pitch?

Hold a level against the roof or the underside of a rafter until it reads level, mark 12 inches along it, and measure from the mark to the roof. That measurement over 12 is the pitch. From the ground, measure the building’s width and the ridge’s height above the wall tops instead.

How do I calculate roof height from the pitch?

Multiply the run by the pitch and divide by 12. On a gable the run is half the building’s width, so a 30-foot-wide house with a 6/12 roof has its ridge 7.5 feet above the wall tops.

What is the formula for roof pitch?

Pitch is the rise divided by the run, times 12, with both in the same unit. A roof that rises 5 feet over a 15-foot run is 4/12.

How do I find the pitch of a shed or lean-to roof?

Use the full width as the run and the difference in wall heights as the rise. A 10-foot-wide shed whose back wall stands 2.5 feet taller than the front has a 3/12 roof.

Sources

  1. International Code Council. 2021 IRC Chapter 9 Roof Assemblies, Section R905 Requirements for Roof Coverings. 2021 IRC
  2. U.S. Department of Labor, Occupational Safety and Health Administration. 29 CFR 1926.500(b) Definitions (Subpart M, Fall Protection). 29 CFR Part 1926 Subpart M, current text on osha.gov
  3. U.S. Department of Labor, Occupational Safety and Health Administration. 29 CFR 1926.501(b)(11) Steep roofs. 29 CFR Part 1926 Subpart M, current text on osha.gov