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.