Roof Pitch Calculator

What roof pitch actually measures

Roof pitch is a ratio, not a length. It compares the vertical rise of the roof to the horizontal run underneath it, and in the US and UK trades that run is fixed at 12 units. A 6/12 roof climbs 6 inches for every 12 inches you travel horizontally. That single ratio decides the angle you cut the rafters, how long those rafters have to be, which roofing materials the manufacturer will warranty, and whether anyone can safely walk on the finished roof.

Three notations describe the same thing. Roofers say "six twelve". Engineers and solar installers use degrees. Drainage and code documents use percent. Converting between them is trigonometry: the angle is the arctangent of rise divided by run, and the percent is simply rise divided by run times 100.

Worked example: a 6/12 roof, every way of saying it

Start with rise 6 and run 12. The ratio is 6 / 12 = 0.5.

Pitch: 0.5 x 12 = 6/12. Angle: arctan(0.5) = 26.57 degrees. Slope: 0.5 x 100 = 50 percent. Note that 50 percent slope is not a 45 degree roof — that catches people out constantly. A 45 degree roof is 12/12, which is 100 percent slope.

Worked example: rafter length for a 24 ft span

The rafter multiplier is the hypotenuse of a right triangle with legs 1 and rise/run, so it equals the square root of 1 + (rise/run) squared. For 6/12 that is the square root of 1.25, or 1.1180. Multiply it by the horizontal run to get the sloped length.

On a simple gable, each rafter only spans half the building. A 24 ft wide house gives a 12 ft run per side. So 12 x 1.1180 = 13.42 ft, or 13 ft 5 in, measured along the roof line from the ridge to the outside of the wall plate. Before cutting, add your eave overhang (commonly 12 to 24 in) and subtract half the thickness of the ridge board, since the calculation runs to the theoretical peak rather than to the face of the ridge.

A few multipliers are worth memorising: 4/12 is 1.0541, 6/12 is 1.1180, 8/12 is 1.2019, 9/12 is exactly 1.25 (the classic 3-4-5 triangle), and 12/12 is 1.4142. The same multiplier converts roof area: a 24 x 40 ft footprint is 960 sq ft of plan area, which at 6/12 becomes 960 x 1.1180 = about 1,073 sq ft of roof surface to shingle, before waste.

Material minimums, and why they exist

Water runs downhill slowly on a shallow roof, and wind pushes it uphill under the shingle laps. That is why every shingle manufacturer publishes a minimum pitch. Standard three-tab and architectural asphalt shingles are approved from 4/12 upward with ordinary underlayment. Between 2/12 and 4/12 they can still be installed, but only with doubled or fully self-adhering underlayment across the deck — miss that detail and the warranty is void. Below 2/12 shingles are not rated at all; that territory belongs to single-ply membranes such as TPO or EPDM, torch-down modified bitumen, or standing-seam metal, which can go down to about 1/4 in per foot on some systems.

Clay and concrete tiles usually want 4/12 or more, slate prefers 6/12 and above, and corrugated metal panels are typically rated from 3/12. Steeper roofs shed water and snow faster, stay drier and last longer — which is exactly why historic buildings in wet and snowy regions have such dramatic roofs.

Walkability

Around 6/12 (26.6 degrees) is the practical limit for walking a dry deck in normal work boots. From 7/12 to 9/12, roofers set up roof jacks or tie off. Above 9/12 the job needs staging and fall protection, and labour quotes rise accordingly. Moss, dew and frost each knock the safe limit down by two or three pitch points.

Measuring your own roof

The safest method uses the attic. Hold a 12 in level horizontally against the underside of a rafter, level it, then measure straight up from the 12 in mark to the rafter. That vertical measurement in inches is your pitch: 7 in means 7/12. Outside, you can do the same against the gable end trim from a ladder.

From the ground, measure the gable end: the total height from the eave line to the peak is the rise, and half the building width is the run. A 5 ft rise over a 15 ft run gives 5/15 = 0.333, or 4/12. Photo protractor apps work too, but only when the picture is taken square to the gable, otherwise perspective flattens the angle.

Limitations worth knowing: hip and valley rafters run diagonally and use a different multiplier (the square root of 2 + (rise/run) squared), so do not cut hips from these numbers. Older roofs sag, so measure at two or three points and use the shallowest reading when checking against a material minimum. And local codes, snow loads and wind zones can override every rule of thumb here — confirm with your building department or a structural engineer before framing.