Hip Roof Calculator

Hip rafter length = (half the width + overhang) x √(2 + slope²); a 40 x 30 ft house at 6/12 needs 24 ft hip rafters and 1,503 sq ft of shingles.

Units
Roof shape
House length
ft
in

Outside of the walls.

House width
ft
in
in

Measured level, past the wall.

in 12

Inches of rise per 12 in of run. The hip rafter length and the pitch multiplier both come from it.

Sets the count of common and jack rafters.

%

A hip roof has four planes and four hips to cut: 15% is a common start, 10% for a gable.

Hip roof area

1,503sq ft

15.03 squares at 6/12, with 24 ft hip rafters and 17 ft 10 ⅝ in common rafters. With 15% waste, order 52 bundles of shingles.
Roof area
1,503sq ft
Hip rafter
24 ft
Common rafter
17 ft 10 ⅝ in
Ridge
10 ft
Hips, all four
96 ft
Ridge cap bundles
4bundles
Dashed: outside of the walls. Ridge and hips in orange.42 ft32 ft

Rafter cut list

RafterLengthCount
Hip24 ft4
Common17 ft 10 ⅝ in16
Jack 12 ft 7 ¼ in8
Jack 24 ft 1 ¼ in8
Jack 35 ft 7 ⅛ in8
Jack 47 ft 1 in8
Jack 58 ft 6 ⅞ in8
Jack 610 ft ¾ in8
Jack 711 ft 6 ⅝ in8
Jack 813 ft ½ in8
Jack 914 ft 6 ⅜ in8
Jack 1016 ft ¼ in8
Jack 1117 ft 6 ¼ in8

Lengths run along the top edge from the ridge line to the tail tip, before ridge board, birdsmouth and plumb-cut deductions. Each jack is longer than the one before by the spacing times the pitch multiplier.

The math
  1. Footprint

    42 ft × 32 ft with overhangs = 1,344 sq ft

  2. Roof area

    1,344 sq ft × 1.118 (pitch multiplier at 6/12) = 1,503 sq ft

  3. Common rafter

    (16 ft half width with overhang) × 1.118 = 17 ft 10 ⅝ in

  4. Hip rafter

    16 ft × √(2 + 0.5²) = × 1.5 = 24 ft

  5. Ridge

    42 ft − 32 ft = 10 ft

  6. Bundles

    15.03 squares × 1.15 waste × 3 bundles, rounded up = 52 bundles

  7. Ridge cap

    106 ft of ridge and hips ÷ 33.3 ft per bundle = 4 bundles

Material list

hip roof, 1,503 sq ft (15.03 squares) at 6/12.

QuantityItem
52bundles

Architectural (laminated) shingles

17.28 squares with 15% waste

4bundles

Hip and ridge cap

106 ft of ridge and hips

4pieces

Hip rafters, 24 ft

16pieces

Common rafters, 17 ft 10 ⅝ in

Hip rafter length = (half the house width + overhang) × √(2 + slope²). For a 40 × 30 ft house with 1 ft overhangs and a 6/12 pitch the hip rafters are 24.0 ft long, the common rafters are 17.89 ft, and the roof has 1,503 sq ft of shingle surface. Switch the shape to Gable to compare the same house with a gable roof.

How the hip roof is calculated

A hip roof slopes on four sides. Every plane has the same pitch, so the roof area is the footprint (walls plus overhangs) times the same multiplier a gable roof uses. What changes is the framing and the trim: the ridge is shorter, and four hips run from the ridge ends to the corners.

Roof area = footprint × √(1 + slope²)  ·  Common rafter = run × √(1 + slope²)  ·  Hip rafter = run × √(2 + slope²)  ·  Ridge = length − width

Worked example: the footprint is (40 + 2) × (30 + 2) = 1,344 sq ft. At 6/12 the multiplier is 1.1180, so the roof is 1,502.6 sq ft, 15.03 squares. The run is half the width with overhang, 16 ft. The common rafter is 16 × 1.1180 = 17.89 ft. The hip rafter is 16 × √(2 + 0.25) = 16 × 1.5 = 24.0 ft. The ridge is 42 − 32 = 10 ft, and the four hips total 96 ft, so ridge cap runs 106 ft.

Hip rafter and jack rafter lengths

The hip rafter runs at 45° in plan, so it is longer than a common rafter over the same rise. Jack rafters fill in between the hip and the wall. Each is longer than the one before by the rafter spacing times the pitch multiplier. At 16 in spacing on this house there are 11 jacks in each of eight sets: the shortest is 2.61 ft, the longest 17.52 ft, and 88 jacks in all, plus 16 common rafters and 4 hips. Lengths here are the theoretical ones along the top edge, from the ridge line to the tail tip. Deduct half the ridge board or hip thickness at the top and lay out the plumb and seat cuts with the rafter calculator.

Hip roof for shingles

Because the hips are cut into the field, a hip roof wastes more shingle than a gable of the same area. The calculator starts at 15% instead of 10%: 15.03 squares × 1.15 = 17.28 squares, or 52 bundles of architectural shingles, plus 4 bundles of hip and ridge cap for 106 ft. TAMKO's 12¼ × 12 in Hip & Ridge covers 100 ft with 3 bundles, so 106 ft needs 3.18 bundles rounded up to 4. For the full list with underlayment and ice barrier use the roofing calculator.

Gable roof calculator

Pick Gable in the roof shape control to run the same house as a gable roof. A gable roof has two planes and a ridge as long as the house plus rake overhangs: 42 ft here, with the same 1,503 sq ft of roof because the overhang is the same all around. The rafter count is higher, since common rafters run the whole length of the building: 31 on each side at 16 in spacing, 62 in all. The gable end wall has a triangle of siding, 112.5 sq ft on this house. Use the siding calculator for that. A gable roof is simpler to frame. A hip roof has eaves on every side, so it needs gutters and soffit all the way round.

Common questions

Does a hip roof have more roof area than a gable? With equal pitch and overhangs, no: the area is the same. It costs more because of the extra cuts and the hips.

Which pitch does a hip roof need? Any pitch that suits the covering: asphalt shingles need at least 2/12 under the 2021 IRC (R905.2.2), with two layers of underlayment below 4/12. Check the number with the roof pitch calculator.

How many squares for the deck? The same 15.03 squares, plus sheets of roof sheathing at 32 sq ft each. Ordering by squares is covered in the roof square calculator.

What to work out next

Steeper, more complex roofs come next: the gambrel roof calculator handles barn roofs and mansards. When the roof is finished, the roof replacement cost calculator shows what a hip roof adds to a re-roof. All roofing tools are grouped in the roofing and siding calculators.