Hip Roof Calculator

How this hip roof calculator works

A hip roof has four sloped faces — two trapezoids on the long sides and two triangles on the short ends — that meet at a ridge running along the long axis. For an equal-pitch hip with a rectangular footprint, this calculator returns:

• The total surface area of all four planes
• The common rafter length (running from eave to ridge on the long sides)
• The hip rafter length (running diagonally from each corner up to the ridge end)
• The ridge length (the horizontal board at the top)
• The equivalent in roofing squares (1 square = 100 sq ft)

Enter the building length, width, eave overhang, and pitch — choose X/12 or degrees — and the geometry is computed instantly.

The math, derived from first principles

The slope factor is the ratio between the actual rafter length and its horizontal run:

slope factor = sqrt(1 + (rise/run)²) = sec(pitch angle)

For a 6/12 pitch the factor is 1.118; for a 9/12 pitch it is 1.250; for a 12/12 (45°) pitch it is 1.414.

Surface area

A neat result: an equal-pitch hip roof has the same surface area as a gable roof with the same footprint and pitch. You can prove this by adding up the four planes — the two trapezoids contribute (W/2)·(2L − W)·sf and the two triangles contribute (W²/2)·sf, which sums cleanly to L·W·sf. So:

hip surface area = (length + 2·overhang) × (width + 2·overhang) × slope factor

Rafter lengths

A common rafter has plan run W/2 (half the width) and rises (W/2)·(rise/run). Its length is the slope factor times the run:

common rafter = (W/2) × slope factor

A hip rafter runs diagonally from a corner to the end of the ridge. Its plan run is (W/2)·√2 (the diagonal of a square with side W/2), and it rises the same height as the common (since both reach the ridge from the eave). So:

hip rafter = (W/2) × sqrt(2 + (rise/run)²)

For a 30 ft × 30 ft pyramid hip with a 6/12 pitch and no overhang, hip rafter = 15 × sqrt(2 + 0.25) = 15 × 1.5 = 22.5 ft.

Ridge length

ridge length = (length + 2·overhang) − (width + 2·overhang) = length − width

The overhangs cancel — only the difference between L and W matters. A 40 × 30 plan gives a 10 ft ridge regardless of overhang.

Standard input checks

• Length and width — measure to the wall (or eave) line, exterior to exterior. The width is always the shorter dimension on a true hip; if width exceeds length, swap them or treat the long dimension as the ridge axis.
• Pitch — IRC R905.2.2 sets a 2/12 minimum slope for asphalt shingles with double-layer underlayment, 4/12 minimum for single-layer. Most American hip roofs run 4/12 to 9/12. Steeper than 9/12 adds a 10–25% labour premium per NRCA contractor surveys.
• Overhang — typical US tract homes are 12 to 18 inches at the eave and 6 to 12 inches at the rake. Ranch and prairie styles often go to 24 inches; modern hip designs sometimes have no overhang at all.

Material and budget context (en-US, 2026)

Once you have the surface area, you can convert to a budget. From recent NRCA, GAF Master Elite, Owens Corning Platinum, and HomeAdvisor / Angi data:

The hip premium covers the extra labour at hip caps, the additional starter and hip ridge accessories (GAF TimberTex, Owens Corning ProEdge), and the higher waste factor (12–15% vs 10% for a gable). For a 1,800 sq ft hip surface in mid-grade architectural shingle, expect roughly $11,500–$13,000 installed including the hip premium.

Common mistakes

Forgetting the hip rafter premium. Hip rafters are the longest rafters on the roof — typically 30–50% longer than commons — and they take a compound cut at top and bottom. Order at least one extra hip rafter beyond the four needed for cull and on-site adjustments.

Treating ridge length as zero on a near-square plan. If length and width are within 2 ft of each other, the ridge is short enough that some framers prefer a pyramid hip with a king post instead — cleaner detail, no ridge board to flash. Run both and compare.

Underestimating waste at the corners. The triangle ends generate the most cut waste — about half the off-cuts of a typical hip roof come from the four hip planes meeting at the ridge ends. Bump waste from 10% (gable) to 12–15% on a hip and to 18–20% on a hip with multiple dormers.

Forgetting the hip-and-ridge cap. A hip needs hip cap shingles down each of the four hip lines plus a ridge cap along the top. That is 4 × hip rafter length + ridge length of cap material — typically 2–4 extra bundles on a mid-sized house.

Code references

• 2026 IRC — R802.4 (rafter spans), R905.2.2 (asphalt shingle slope), R905.7 (slate), R908 (reroofing).
• NRCA Roofing Manual: Steep-Slope Assemblies — hip and ridge cap installation, fastening patterns, and ventilation requirements.
• ASTM D3462 for asphalt shingles, ASTM C1167 for clay tile, ASTM C1492 for concrete tile.

Putting it together

Run the calculator, write down the surface area, the rafter lengths, and the ridge length, and use them as the foundation for the structural take-off and the materials order. Cross-check the area with the roof area calculator, size the framing with the roof truss calculator, and estimate the budget with the roof cost calculator. For a head-to-head comparison with a gable, run both shapes through the roof square footage calculator — you will see the area is identical but the linear footage of cap and hip is what drives the cost difference.

The hip is the workhorse roof of mid-century American architecture. Get the geometry right at this stage and every downstream cost — material, labour, waste, accessories — falls into a tight, defensible range.