Hip Roof Area Calculator

How the hip roof area calculator works

A hip roof slopes down on all four sides: two trapezoid faces along the long sides, two triangles at the ends, meeting at a ridge. When every face has the same pitch, the sloping area of the whole roof is simply its plan area divided by the cosine of the pitch, the same pitch multiplier used for any pitched roof:

A = L × W ÷ cos θ

L and W are the plan length and width, measured to the outside of the eaves, and θ the pitch. It does not matter that the faces are different shapes; each one's sloping area is its plan area times the same multiplier, so the total is too. The calculator also works out the lengths used to set out and order the roof: the rise, the common rafter, each hip, the ridge, and the total length of hips and ridge.

Hips, ridge and rafters

Each face rises over half the shorter side, the span. With r for half the span, the rise is r × tan θ and the common rafter r ÷ cos θ. A hip runs diagonally from a corner to the end of the ridge, so on plan it covers r in both directions, and its true length is √(2r² + rise²). The ridge is the long side minus the span; on a square plan it vanishes and the roof becomes a pyramid.

Pitch is given in degrees here. To convert from the rise-over-run figure roofers in the US use, θ = tan⁻¹(rise ÷ 12): 4 in 12 is 18.43°, 6 in 12 is 26.57° and 12 in 12 is 45°. The pitch multiplier is then √(1 + (rise ÷ 12)²), which gives 1.054, 1.118 and 1.414 for those three pitches, the same as dividing by the cosine of the angle.

Worked through

With the metric defaults, a 10 × 6 m plan at 30°: the plan area is 60 m², the multiplier 1 ÷ cos 30° = 1.155, so the roof is 69.28 m². Half the span is 3 m, so the rise is 3 × tan 30° = 1.73 m, the common rafter 3 ÷ cos 30° = 3.46 m, each hip √(18 + 3) = 4.58 m and the ridge 10 − 6 = 4 m. Hips and ridge together come to 22.33 m.

With the US defaults, a 33 × 20 ft plan at 6 in 12 (26.57°): 660 ft² times 1.118 is 737.9 ft², or 7.38 roofing squares of 100 ft². The rise is 5 ft, the common rafter 11.18 ft, each hip √(200 + 25) = 15 ft and the ridge 13 ft, so 73 ft of hips and ridge. At 6 2/3 in of exposure and 5% waste, that is 138 ridge caps, or four bundles of 45, in the ridge cap calculator.

Measure to the eaves

The roof covering runs past the walls to the edge of the eaves, so the plan length and width should be the building's footprint plus the overhang on each side. It makes a real difference: the same 10 × 6 m building with 300 mm eaves all round is a 10.6 × 6.6 m plan, and 80.78 m² of roof, about 17% more than the footprint alone suggests. Measured this way, the rafter and hip lengths run all the way to the eaves edge, overhang included, and the rise is from the eaves edge up to the ridge. With those 300 mm eaves, the 30° common rafter grows from 3.46 m at the wall line to 3.81 m, and each hip from 4.58 m to 5.04 m; the ridge stays 4 m.

Pitch limits for the covering

Every roof covering has a lowest pitch it can be laid at, and a hip roof's faces are all the same pitch, so one check covers the roof. In the US, section R905.2.2 of the International Residential Code allows asphalt shingles only at 2 in 12 or steeper, and asks for double underlayment from 2 in 12 up to 4 in 12. The calculator shows the pitch in both degrees and inches in 12 and flags which band it falls in. Tiles have their own minimums from the maker: Marley's Modern concrete tile, for example, goes down to 17.5° in its smooth finish, about 3.8 in 12, with a higher minimum for granular finishes.

What this tool does not do

It assumes a regular hip roof with every face at the same pitch and a rectangular plan. L-shaped plans, dormers, valleys, and roofs with different pitches front and back need their sections worked out separately. The area has no waste allowance; add what the covering maker recommends for the cuts at hips and edges when you order.

Using this calculator with other BuildMetricLab tools

The ridge cap calculator turns the hips and ridge length into caps, the roof pitch calculator converts between degrees and rise over run, and the rafter set-out calculator marks out the rafters. All BuildMetricLab tools run in your browser with no sign-up, and the formula is on the page so the maths can be checked.