Roof Pitch Calculator
Roof pitch is the language everything else on a roof speaks, rafters, shingle amounts, and how steep it'll feel to walk. Enter your rise and run below and the calculator fills in the rest: the pitch as x-in-12, the slope angle in degrees, the rafter length, and the multiplier you need to turn a flat footprint into true roof area.
How this is calculated
Pitch is expressed as rise over a 12-inch run, so a roof that climbs 6 inches for every 12 of run is a 6/12 pitch. The slope angle is the arctangent of rise divided by run. Rafter length comes straight from the Pythagorean theorem: the square root of rise squared plus run squared. The area multiplier, rafter length divided by run, is what you multiply a flat footprint by to get the actual sloped surface area for materials.
A worked example
A roof with a 6-inch rise over a 12-inch run is a 6/12 pitch. The angle works out to about 26.6 degrees. The rafter length over that 12-inch run is the square root of 6 squared plus 12 squared, about 13.4 inches, and the area multiplier is roughly 1.118. So a 1,000 square-foot footprint is about 1,118 square feet of actual roof. The calculator does all of this from the two numbers you enter.
Common questions
It's how steep a roof is, written as inches of vertical rise per 12 inches of horizontal run. A 4/12 is a gentle slope; a 12/12 rises at 45 degrees. Enter rise and run above to get yours.
Take the arctangent of rise divided by run. A 6/12 pitch is about 26.6 degrees, a 12/12 is 45. The calculator shows the angle automatically.
It's the hypotenuse of the triangle formed by rise and run: the square root of rise squared plus run squared. Enter your rise and run and the tool returns the rafter length directly.
A steeper roof has more actual surface than its flat footprint, so you need the slope multiplier to order the right amount of shingles or sheathing. This calculator gives you that multiplier.
Estimates for planning. Verify against your supplier's units and your local building codes before ordering or building. For anything structural, follow your engineer or local code.