The formula

The plan with its overhang: (length + 2 × overhang) × (width + 2 × overhang).
Times the pitch factor: √(1 + (rise ÷ 12)²). A 6/12 roof is √1.25 = 1.118, so it has 11.8% more area than its plan. On a rectangle the result is the same for a gable, a hip and a shed roof: the pitch sets the area, the type sets the edges.
Plus waste: a percentage on top for cutting.
Squares and bundles: divide by 100 ft² for squares, multiply by the bundles per square on the wrapper, and round up.
Edges: a gable has a ridge the length of the roof, eaves on both long sides and four sloped rakes. A hip has a shorter ridge (length less width), four hips and eaves all round. A shed has one eave and two rakes. Drip edge goes along the eaves and rakes.

The defaults and their sources3 bundles per square and 35 ft of hip and ridge per bundle of cap shingles come from Mike Guertin's estimating guide in Fine Homebuilding, "Don't fall short on shingles" (November 2002): three bundles to a square is the most common packaging, while heavier laminated shingles take four or five. The 5% waste default is the same article's figure for fall-off along gable ends, valley trimmings and damaged shingles; it says a complex roof with valleys needs more. Neither GAF nor Owens Corning publishes a waste percentage by roof type, so the calculator does not change waste with the type: enter your roofer's or supplier's figure. The pitch check follows the International Residential Code, section R905.2.2: asphalt shingles only at 2/12 or steeper, with extra low-slope underlayment from 2/12 up to 4/12. Check the edition your area has adopted.

Worked example

A 50 × 30 ft house with a 1 ft overhang has a 52 × 32 ft roof plan, 1,664 ft². At 6/12 the pitch factor is 1.118, so the roof is 1,860 ft², or 18.6 squares. Add 5% waste: 1,953 ft², 19.5 squares, and at 3 bundles a square 59 bundles. As a gable it has a 52 ft ridge (2 bundles of cap), 104 ft of eaves and four 17 ft 11 in rakes, 176 ft of drip edge. As a hip roof the area and bundles are the same, but the ridge is 20 ft with four 24 ft hips (4 bundles of cap) and 168 ft of eaves. The roof rises 8 ft from eave to ridge at 26.6°.

Pitch factor and angle by pitch (worked with the calculator)
Pitch	Pitch factor	Angle	Roof area per 1,000 ft² of plan
3/12	1.031	14.0°	1,031 ft²
4/12	1.054	18.4°	1,054 ft²
6/12	1.118	26.6°	1,118 ft²
8/12	1.202	33.7°	1,202 ft²
10/12	1.302	39.8°	1,302 ft²
12/12	1.414	45.0°	1,414 ft²

Shingles for common houses: 1 ft overhang, 5% waste, 3 bundles a square (worked with the calculator)
House	Roof	Roof area	Squares with waste	Bundles
24 × 32 ft cabin	8/12 gable	1,062 ft²	11.2	34
40 × 30 ft	4/12 gable	1,417 ft²	14.9	45
40 × 30 ft	8/12 gable	1,615 ft²	17.0	51
48 × 28 ft	6/12 hip	1,677 ft²	17.6	53
50 × 30 ft	6/12 gable or hip	1,860 ft²	19.5	59
60 × 40 ft, 1½ ft overhang	6/12 gable	3,029 ft²	31.8	96

Beyond the shingles

Underlayment covers the whole roof area; check its roll coverage, and the extra underlayment the IRC asks for under 4/12.
Starter strip runs along the eaves (and often the rakes): use the eave and rake lengths above.
Hip and ridge cap is sold by the bundle in linear feet; the calculator counts 35 ft a bundle.
Dormers, valleys and chimneys are not in a rectangle. Measure each extra plane, add it, and allow more waste for the valley cuts.
Measure the real roof when you can. The footprint method assumes one pitch and an even overhang; an aerial roof report or a roofer's takeoff measures each plane.

Start from the floor plan

The roof sits on the house's outside walls, so its plan is the footprint plus the overhang. Draw the footprint in FloorGen and read its outside length and width off the plan; "Open the footprint as a plan" in the calculator builds it for you. See how to draw a floor plan and exterior elevation drawings for the roof seen from the side.

Questions

How do I calculate how many squares my roof is?

Multiply the roof plan (the footprint plus the overhang on every side) by the pitch factor, √(1 + (rise ÷ 12)²), and divide by 100. A 52 × 32 ft plan at 6/12 is 1,664 × 1.118 = 1,860 ft², 18.6 squares, before waste.

How many bundles of shingles are in a square?

Three for most shingles, which is the most common packaging. Heavier laminated shingles can take four or five bundles a square. The coverage is printed on each bundle's wrapper.

Does a hip roof need more shingles than a gable roof?

On the same rectangle at the same pitch, the area is the same. A hip roof has more cut edges along its hips, so it wastes more, and it needs more hip and ridge cap: 116 ft of hip and ridge on the 50 × 30 ft example against 52 ft of ridge for the gable.

What is the lowest pitch for asphalt shingles?

2/12 under the International Residential Code (R905.2.2). From 2/12 up to 4/12 it calls for extra, low-slope underlayment; below 2/12, use a low-slope roofing system instead of shingles.

How do I convert roof pitch to degrees?

The angle is the arctangent of rise ÷ 12: 4/12 is 18.4°, 6/12 is 26.6°, 8/12 is 33.7° and 12/12 is 45°. The calculator shows it for any rise.

Roofing calculator