Roofing Calculator

How to measure a roof from the ground

You don’t need to climb onto the roof. A roof’s surface is its footprint seen from above, stretched by the slope, so three measurements taken on the ground are enough:

1. Length and width of the building, measured along the outside of the walls. For a gable or shed roof, the width is the direction the roof slopes in.
2. Overhang: how far the eaves and gable ends reach past the walls, measured level. The calculator adds it on all four sides.
3. Pitch: in the US, the rise in inches for every 12 inches of horizontal run (a 6 in 12 roof climbs 6 inches per foot); elsewhere usually an angle in degrees. A pitch gauge or a smartphone level app held on a rafter or the gable trim gives either.

Then set a waste allowance for off-cuts and the number of bundles per square printed on the shingles you plan to buy. The result shows the roof area, the number of squares and bundles, and the rafter length.

Roof area formula

rise ÷ run

the pitch as a ratio (6 in 12 = 0.5)

θ

the pitch angle; rise ÷ run = tan θ

L, W, o

building length, width and overhang

b

bundles per square

Every plane of a roof with a single pitch is tilted by the same angle, so its true surface is its footprint multiplied by the same factor k. That holds for a hip roof too: the four planes have different shapes, but when they share one pitch, the total surface is still the whole footprint times k. The roof type only changes the rafter, hip and ridge lengths.

A shed roof’s rafter runs the whole width: (W + 2o) × k. On a hip roof, W is the shorter side, the hips meet the corners at 45° in plan, and the ridge is the difference between length and width.

Worked example

A 40 ft × 30 ft house with a 12-inch overhang and a 6 in 12 gable roof, 10% waste, 3 bundles per square:

1. Footprint with overhang: (40 + 2) × (30 + 2) = 42 × 32 = 1,344 ft²
2. Slope factor: √(1 + 0.5²) = √1.25 = 1.1180
3. Roof area: 1,344 × 1.1180 = 1,502.6 ft² (139.6 m²), or 15.03 squares
4. With 10% waste: 15.03 × 1.1 = 16.53 squares
5. Bundles: 16.53 × 3 = 49.6, so 50 bundles
6. Rafter length: (15 + 1) × 1.1180 = 17.89 ft (17 ft 10.7 in); the pitch is 26.57°

As a hip roof, the area and bundles stay the same; the ridge shrinks to 40 − 30 = 10 ft and each hip rafter is 16 × √(2 + 0.25) = 24 ft.

In metric, a 12 m × 9 m house with a 30 cm overhang and a 30° roof: 12.6 × 9.6 = 120.96 m² × 1.1547 = 139.67 m², which is 1,503.4 ft², 15.03 squares and, with 10% waste, 50 bundles.

Squares, bundles and waste

In North America, roofing is sold and priced by the square: 100 square feet of roof, about 9.29 m². Asphalt shingles come in bundles, and for most standard three-tab and laminated (architectural) shingles three bundles cover one square. IKO, for example, packs its Cambridge laminated shingles 20 to a bundle so that three bundles cover 100 ft². Not every product works out that neatly: IKO itself points out that three bundles of some other shingles cover only about 98.4 ft², and other products are packed differently. Coverage is printed on the wrapper, so enter the figure for the shingles you are buying.

The waste allowance covers shingles cut off at rakes, hips and valleys and a few damaged ones. This calculator starts at 10%, which is a starting point rather than a standard: a plain gable roof wastes less than a roof with hips, valleys and dormers, where every edge is a cut. Your supplier or roofer can tell you what they allow for your roof.

What the estimate leaves out

• Complex roofs. Dormers, intersecting wings, valleys and planes with different pitches need to be measured separately and added up. Split the footprint into rectangles, as you would with the square footage calculator, and run each part.
• Low slopes. Shingles shed water only when the roof is steep enough. IKO’s instructions for its Cambridge shingles say never to apply them below 2 in 12 and call for special underlayment from 2 in 12 up to 4 in 12; other manufacturers set their own limits. Flatter roofs use membranes, which are also sold by area.
• Openings. Chimneys and skylights are not subtracted; they are small and the cutting around them uses up most of what they save.
• Rafter details. Rafter lengths are geometric lengths along the slope. The ridge board, the birdsmouth and plumb cuts and the fascia change the length you cut; follow your framing plan or local building code.
• Prices. The calculator gives quantities, not costs, because material and labor prices vary too much by region and product to estimate honestly.