Hip Roof Calculator

Why a Hip Roof Takes More Figuring

On a gable roof, every rafter is the same and the ends of the building are flat walls. A hip roof slopes down on all four sides, which sheds wind better and gives the eaves a continuous line around the house, but it adds pieces that don't exist on a gable: four hip rafters running diagonally from the corners up to the ridge, a ridge that is shorter than the building, and jack rafters that shrink in length as they approach each corner. Getting those numbers right before ordering saves a second trip to the lumber yard.

Step by Step

Measure the building's length and width at the outside of the wall plates. Enter the pitch as inches of rise per 12 inches of run, the same way it appears on plans (6 for a 6/12 roof). Add the eave overhang as a level, horizontal distance out from the wall, since that is how it's usually specified on drawings; leave it at 0 for none. Finally, pick a waste allowance for roofing material. Hip roofs typically call for 10–15% because every hip line produces angled cuts and short leftover pieces.

The Formula Explained

For a regular hip roof (all four sides at the same pitch, rectangular footprint), each common rafter covers a run of half the width, so its length is run × √(1 + (pitch ÷ 12)²). That square-root term is the slope factor. Because the hips rise to meet the ridge at 45° in plan, the ridge is simply length − width, and it becomes zero on a square building, which turns into a pyramid.

The hip rafter travels the diagonal of each 12-inch square of common run, which is 12 × √2 ≈ 16.97 inches. This is why framers lay out hips using a 17-inch unit run on the framing square instead of 12. The exact hip length is run × √(2 + (pitch ÷ 12)²). The overhang is added to the run for both rafters. The total roof area is the plan area inside the drip edge multiplied by the slope factor, because every face shares the same pitch; divide by 100 for roofing squares.

A Real Example

Take a 40 ft × 28 ft house with a 6/12 pitch and a 1 ft overhang. The ridge is 40 − 28 = 12 ft. With the overhang, the common rafter covers 14 + 1 = 15 ft of run; the slope factor for 6/12 is √1.25 = 1.118, so the common rafter is 16.77 ft. The hip is 15 × √2.25 = 22.5 ft. The framing-square shortcut agrees closely: √(17² + 6²) ≈ 18.03 inches of hip per foot of common run (exactly 18.00 with 16.97 instead of 17), times 15 ft. The drip-edge footprint is 42 × 30 = 1,260 sq ft, times 1.118 gives 1,409 sq ft, or 14.09 squares, and 15.50 squares after 10% waste.

Edge Cases to Watch For

These are theoretical line lengths to the ridge centerline. Actual cut lengths are shortened by half the ridge thickness for commons and by a slightly larger amount for hips (measured on the 45°), so check the deduction for your lumber before cutting. Irregular hips (different pitches on ends and sides) and L-shaped footprints with valleys don't follow these formulas. If you enter a width larger than the length, the calculator swaps them, since the ridge always runs along the longer side. It covers geometry and material quantities only, not rafter sizing, spacing, or structural loads, which should come from your local code's span tables or an engineer.