Hip Roof Calculator
Enter the footprint, the pitch and the overhang. You get the sloped roof area, squares, shingle bundles, ridge length, the length of all four hip lines and the eave perimeter — plus the slope multiplier behind each number, so you can check it by hand.
What a hip roof actually is, in numbers
A hip roof is four planes over a rectangle. The two long planes are trapezoids that run down to the eaves on the long sides; the two ends are triangles that run down to the eaves on the short sides. All four planes share the same pitch, and that single constraint is what makes the whole roof solvable with one multiplier.
The consequence is worth stating plainly, because it is where most hand estimates go wrong: the sloped area of a hip roof equals its flat footprint multiplied by the slope multiplier. Not approximately — exactly, as long as all four planes have the same pitch. You can prove it by adding the two trapezoids and the two triangles; the algebra collapses to length × width × multiplier. Everything else the calculator returns is a length along a ridge or a hip line, and those come from the same right triangles.
Pitch, multiplier and angle for every common roof slope
The table below is the one number people actually reuse. Find your pitch in the first column, multiply your footprint by the second column, and you have the sloped area. The last column does the same job for a 100 sq ft section of footprint, which is handy when you are pricing by the square rather than by the square foot.
| Pitch (rise per 12) | Slope multiplier | Angle | Roof area per 100 sq ft footprint |
|---|---|---|---|
| 1/12 | 1.003 | 4.76 | 100.3 |
| 2/12 | 1.014 | 9.46 | 101.4 |
| 3/12 | 1.031 | 14.04 | 103.1 |
| 4/12 | 1.054 | 18.43 | 105.4 |
| 5/12 | 1.083 | 22.62 | 108.3 |
| 6/12 | 1.118 | 26.57 | 111.8 |
| 7/12 | 1.158 | 30.26 | 115.8 |
| 8/12 | 1.202 | 33.69 | 120.2 |
| 9/12 | 1.25 | 36.87 | 125 |
| 10/12 | 1.302 | 39.81 | 130.2 |
| 11/12 | 1.357 | 42.51 | 135.7 |
| 12/12 | 1.414 | 45 | 141.4 |
How each result is derived
All of it follows from one triangle. The run is half the width, because a symmetrical hip roof rises from both eaves to a ridge in the middle. The rise is the run times the pitch divided by 12. The slope length is the run times the multiplier. From there:
- Roof area = effective length × effective width × multiplier, where the effective dimensions include the overhang on both sides.
- Ridge length = effective length − effective width. Each hip end eats half a width, so the ridge is one full width shorter than the building. On a square plan the ridge length is zero and the roof is a pyramid.
- Each hip line = √((width ÷ √2)² + rise²). A hip corner travels diagonally up to the end of the ridge, so its horizontal travel is the width divided by the square root of two, not the width itself. This is the single most common place a hand-taken-off hip length comes out short.
- Eave length = 2 × (effective length + effective width). This is your fascia, drip edge and gutter run, not the wall perimeter.
- Rise at the ridge = run × pitch ÷ 12. Useful when you need to check that the ridge height clears a window head or a second-floor ceiling.
Every one of those formulas is in the page source and in the test suite, and the pitch table is recomputed from √(1 + (rise ÷ 12)²) on every build. If a number in the table ever drifted from the formula, the build fails before anything is published.
Measuring the footprint correctly
Measure the outside face of the framed walls, wall to wall, on the long side and on the side the roof spans. Do not use interior room dimensions: wall thickness, sheathing and finish all make the inside smaller, and on a small building the difference is larger than the rounding in any shingle order.
Then measure the overhang. It is the horizontal distance from the wall to the fascia, and it must be measured horizontally — not along the slope. A 12 in overhang adds 1 ft to each side, so 2 ft to the length and 2 ft to the width. On a 40 × 24 ft building with a 6/12 pitch and a 1 ft overhang, the footprint becomes 42 × 26 ft and the roof area is 42 × 26 × 1.118 = 1,221 sq ft. Skipping the overhang would understate the same roof by about 148 sq ft, which is nearly a square and a half of shingles.
From area to bundles
Roofing is sold by the square, where one square is 100 sq ft of finished roof. Standard three-tab and most architectural shingles cover three bundles to the square; some designer lines run four or five, and the field is on the bundle wrapper, so check it rather than assuming. The calculator takes the area, applies your waste allowance, divides by 100 and rounds up to whole bundles, because suppliers do not sell fractions of a bundle.
Waste is not padding. A plain rectangular hip roof, four planes and four hips, cuts cleanly at about 10%. Add valleys, dormers, a chimney saddle or a change of pitch and 15% is realistic. Hip-and-ridge cap is bought by the linear foot and is not included in the bundle count: add the ridge length plus the four hip lengths, and allow a little extra for the laps at the ridge ends.
Five mistakes that show up in real orders
- Using the floor area as the roof area. A 24 × 40 ft building is 960 sq ft on the floor and 1,221 sq ft of roof at 6/12 with a 1 ft overhang. The multiplier and the overhang together are a 27% difference.
- Measuring the overhang along the slope. The horizontal projection is the number the area formula needs; the sloped length is longer and inflates the footprint.
- Taking the hip length as width ÷ 2. The hip runs diagonally across the corner plan, so its horizontal travel is width ÷ √2 — about 41% longer than half the width.
- Forgetting that the ridge is shorter than the building. Ordering ridge cap to the building length overbuys by a full width on every roof.
- Rounding down on bundles. A roofer one bundle short on a Friday afternoon loses a day. Rounding up costs a few dollars and a trip back to the supplier that you will not make.
What this calculator does not do
It assumes one uniform pitch and a simple rectangle. It does not handle an offset ridge, two different pitches meeting at a valley, L-shaped plans, curved or conical roofs, or the extra material for ice-and-water shield, underlayment laps and starter course, all of which are quoted separately by the roll or the linear foot. For an L-shaped plan, break the roof into rectangles at the valleys, run each one, and add the results — the ridge and hip lengths will be right per rectangle, but the shared valley will need a separate allowance.
Estimates only. These figures are geometric, not a material takeoff and not a structural design. Spans, rafter sizes, nailing and bracing must be checked against your local building code and, for anything structural, by a licensed engineer or contractor. Verify quantities against the supplier's coverage figures before ordering.