A gable roof over a 24-foot-wide house at a 6/12 pitch rises 6 feet to the ridge, slopes at 26.57° and needs common rafters 13' 5" long, or 14' 6⅜" with a 12-inch overhang. Over a 40-foot house that is about 1,163 square feet of roof, 11.6 squares. The calculator works the same numbers for gable, hip and shed roofs from whichever value you know: the pitch, the angle, the ridge height or the slope in percent.
Pitch, angle, rise and percent are the same slope
Pitch is written as rise over run: a 6/12 roof rises 6 inches for every 12 inches of horizontal run. The same slope can be given as an angle (atan of 6 ÷ 12 = 26.57°), as a percent (6 ÷ 12 × 100 = 50 %) or as the ridge height over a known span. Pick what you know in the second step; when you switch, the current slope carries over so the result does not jump.
| Pitch | Angle | Slope | Slope factor |
|---|---|---|---|
| 3/12 | 14.04° | 25.0 % | 1.031 |
| 4/12 | 18.43° | 33.3 % | 1.054 |
| 5/12 | 22.62° | 41.7 % | 1.083 |
| 6/12 | 26.57° | 50.0 % | 1.118 |
| 7/12 | 30.26° | 58.3 % | 1.158 |
| 8/12 | 33.69° | 66.7 % | 1.202 |
| 9/12 | 36.87° | 75.0 % | 1.250 |
| 10/12 | 39.81° | 83.3 % | 1.302 |
| 12/12 | 45.00° | 100.0 % | 1.414 |
The slope factor is how much longer the roof surface is than its plan: rafter length ÷ run, or 1 ÷ cos(angle). Multiply a plan area by it to get the roof area.
How to find the pitch of an existing roof
Hold a level horizontally against a rafter or the roof surface, measure 12 inches along the level and measure straight down from that mark to the roof. That distance in inches is the pitch. From the ground you can also measure the ridge height above the top of the walls and the span: enter them in "Rise" mode. A ridge 5 feet above the walls over a 28-foot span is a 4.29/12 pitch, 19.65°.
Rafter length
The run of a gable or hip rafter is half the span; on a shed roof it is the whole span. The rafter along its centerline is run ÷ cos(angle). The eave overhang is entered as a horizontal distance, as it appears on plans, so the rafter with overhang is (run + overhang) ÷ cos(angle). A 12-inch horizontal overhang at 6/12 adds 13.42 inches along the slope and drops the eave 6 inches below the top of the wall.
These are lengths on the rafter centerlines. The finished ridge sits higher by the depth of the rafter and the roof build-up, and the rafter is cut longer at the plumb cut and the birdsmouth. Sizing the rafters themselves depends on snow and wind loads: use the span tables in IRC R802 or an engineer's design.
Hip roofs
On a hip roof the main planes behave like a gable. The hip ends slope from the end walls to the ridge; their horizontal run is half the span when all planes share one pitch, which leaves a ridge equal to the house length minus the span: 40 − 24 = 16 feet in the example. You can set a different hip run for a steeper or flatter hip. The hip rafter lies over the plan diagonal √((span/2)² + run²), so at 6/12 over a 24-foot span it is 18' 0" long and slopes at 19.47°, flatter than the common rafters. The calculator keeps the eave level all round, so the overhang along the hip ends is scaled with the hip run.
Roof area and squares
The roof area adds every plane with its overhangs: plan area ÷ cos of the plane's angle. Gable ends are counted without a rake overhang. Roofing is sold by the square, 100 square feet of roof surface. The 24 × 40-foot gable roof above is 11.6 squares; the same house with a hip roof is 12.2 squares, because the overhang runs round all four sides. Add waste for starter courses, ridge caps and cuts when you order.
Minimum pitch for the covering
Every roofing material has a lowest slope at which it sheds water. The IRC sets them in Chapter 9: asphalt shingles from 2/12, and between 2/12 and 4/12 they need two layers of underlayment (R905.1.1, R905.2.2); clay and concrete tile from 2½/12; metal roof shingles, wood shingles and lapped metal panels from 3/12; slate from 4/12; standing-seam metal from ¼/12. Choose your covering and the result card flags a pitch that is too low, including the hip ends.
Common mistakes
- Using the full span as the run of a gable rafter. The run is half the span.
- Measuring the overhang along the slope and entering it as horizontal. At 6/12 a 12-inch horizontal overhang is 13.42 inches along the rafter.
- Treating pitch and angle as proportional: 12/12 is 45°, but 6/12 is 26.57°, not 22.5°.
- Laying shingles on a 3/12 roof with one layer of underlayment.
Pouring a slab or footings for the building? The Concrete Calculator works out the cubic yards and bags.