Hip Roof Calculator

A hip roof calculator finds the roof surface from the footprint and the pitch. The footprint is length × width, and the pitch turns that flat area into a sloped one with a multiplier. A 40 × 30 ft footprint at 6/12 pitch has a multiplier of 1.118, so the roof is 40 × 30 × 1.118 = 1,341.64 sq ft.

The formula in plain words

Picture the roof laid on the ground as a flat rectangle. Tilt it up to the pitch and the surface stretches, because a slope is longer than the ground under it.

The stretch is the multiplier. For a roof that rises 6 inches for every 12 inches of run, the slope is the hypotenuse of a 6 by 12 triangle, which is the square root of (6² + 12²) = 13.42 inches. Divide by 12 and you get 1.118.

A hip roof slopes on all four sides. Its area still equals the footprint times that multiplier, which is the same result as a gable roof with the same footprint and pitch.

Worked examples

Example 1, the default: 40 ft by 30 ft footprint at 6/12.

• Multiplier: 1.118
• Area: 40 × 30 × 1.118 = 1,341.64 sq ft
• Squares: 1,341.64 ÷ 100 = 13.4
• Bundles: 1,341.64 ÷ 33.33 = 40.25, rounded up to 41

Example 2, a steeper roof: 36 ft by 28 ft footprint at 8/12.

• Multiplier: square root of (1 + (8 ÷ 12)²) = 1.202
• Area: 36 × 28 × 1.202 = 1,211.47 sq ft
• Squares: 12.1
• Bundles: 36.34, rounded up to 37

Pitch multipliers

Pitch (rise per 12)	Multiplier
3/12	1.031
4/12	1.054
5/12	1.083
6/12	1.118
8/12	1.202
10/12	1.302
12/12	1.414

How to measure

Measure the footprint at the outside edge of the eaves. If you cannot get on the roof, measure the walls and add the overhang on each side. A 40 × 30 ft house with 1 ft overhangs has a 42 × 32 ft roof footprint.

For pitch, hold a level 12 inches out from the roof surface at the underside of a rafter in the attic and measure straight down to the rafter. That drop is the rise. The roof pitch calculator converts rise and run to the pitch value and angle.

Common mistakes

• Measuring only the walls and forgetting the overhang.
• Using the roof area for ordering shingles without adding for hips. Many roofers add 10% to 15% on a hip roof because of the extra cutting.
• Treating a roof with a dormer or a bump-out as one rectangle. Split it into separate sections and add them.
• Ignoring the ridge cap. Hips and the ridge need cap shingles, which are priced by the linear foot, separate from the field area.
• Using the pitch angle in degrees when the formula wants rise per 12 inches.

Hip and ridge cap

Area does not tell you how much cap shingle to buy. On a hip roof, cap runs along the four hips and the ridge. With equal pitch on all sides, a 40 × 30 ft hip roof at 6/12 works out like this:

• Each hip covers a horizontal run of 15 × 1.414 = 21.2 ft and rises 15 × 6 ÷ 12 = 7.5 ft
• Hip length: the square root of (21.2² + 7.5²) = 22.5 ft
• Four hips: 4 × 22.5 = 90 ft
• Ridge: 40 − 30 = 10 ft
• Total cap: 100 ft

Add a little for overlaps and cuts. Complicated roofs are worth measuring on site.

Hip roof or gable, for ordering

If you are comparing the two shapes for a budget, the shingle area is the same, so the choice comes down to framing and looks. A hip roof sheds wind better and has no gable ends to side, and it usually costs more to frame. For the shingles themselves, enter the same footprint and pitch for both and expect nearly the same bundle count.

Related calculators

Once you have the area, the roofing shingle calculator turns it into bundles and cost. The roof area calculator covers the gable case, and the gambrel roof calculator handles a barn-style shape. For rafter lengths, try the rafter calculator.