Roof Pitch

What the Roof Pitch Calculator Does

This calculator converts a roof's slope between two common formats: the rise-in-12 ratio used on building plans (for example, 4:12) and the slope angle in degrees. Enter the vertical rise and the horizontal run, and it returns both the standard pitch notation and the angle of the roof surface.

It is built for roofers, DIY homeowners, framers, solar installers, and inspectors. If you are ordering shingles, sizing rafters, checking ladder safety, or estimating snow load, knowing the exact pitch and angle is the starting point for every other calculation.

How Roof Pitch Is Calculated (The Formula)

Roof pitch is the ratio of vertical rise to horizontal run. In the United States it is almost always expressed per 12 inches of run, so the rise-in-12 figure is the rise scaled to a 12-unit run:

ratio (rise-in-12) = (rise / run) x 12

The angle of the roof in degrees comes from the inverse tangent (arctangent) of rise divided by run:

angle = atan(rise / run), converted from radians to degrees by multiplying by 180 / pi.

Because both formulas depend only on the rise-to-run ratio, the units cancel: inches, feet, or meters all give the same pitch and angle as long as rise and run use the same unit.

Worked Example With Real Numbers

Suppose a roof rises 6 feet over a horizontal run of 18 feet. Plug the numbers into each formula:

Rise-in-12 = (6 / 18) x 12 = 0.3333 x 12 = 4. So the pitch is 4:12.

Angle = atan(6 / 18) = atan(0.3333) = 18.43 degrees.

This roof reads as a '4 in 12' pitch and slopes at about 18.4 degrees. A steeper roof rising 9 feet over the same 18-foot run would be a 6:12 pitch at roughly 26.57 degrees.

Common Roof Pitch Reference Points

These conversions help you sanity-check the calculator's output and understand which roofing materials suit a given slope:

• 1:12 = 4.76 degrees (very low slope; needs membrane roofing, not standard shingles)
• 4:12 = 18.43 degrees (common, walkable, the typical minimum for asphalt shingles)
• 6:12 = 26.57 degrees (moderate, popular on residential homes)
• 9:12 = 36.87 degrees (steep; harder to walk, often requires roof jacks)
• 12:12 = 45 degrees (a true 45-degree roof where rise equals run)

Tips and Common Mistakes

The most frequent error is confusing run with the rafter length. Run is the horizontal distance from the wall to a point directly below the ridge, not the diagonal slope of the rafter. For a symmetrical gable roof, the run is half the total building width, not the full span.

Also keep rise and run in the same unit, and remember that '12:12' is not double '6:12' in terms of angle. Pitch ratios are linear, but the angle follows the tangent curve, so equal ratio steps produce smaller and smaller angle gains as the roof steepens.

Factors That Affect Your Result

Real roofs can vary across their surface due to settling, framing tolerances, or sagging, so measure in a few spots and use a representative figure. When measuring an existing roof, a 12-inch level held horizontally with a tape measuring the rise at the 12-inch mark gives the rise-in-12 directly.

Material choice depends heavily on the result: low slopes below about 2:12 generally require continuous membranes rather than overlapping shingles. Always confirm minimum-slope requirements with your local building code and the manufacturer's installation instructions before ordering materials.