Hip Roof Calculator

Enter your building dimensions, roof pitch and eave overhang to estimate roof area, rafter lengths and roofing materials. The diagram shows where to measure.

Calculate

This calculator models a regular hip roof: a rectangular plan, level eaves, equal pitch on all four faces and an equal horizontal overhang on every side. That covers the most common hip roof and produces theoretical line geometry you can check against a quote. It is a planning model, not a structural design or a full timber cut list.

How to Measure a Hip Roof

Wall measurements vs. eave measurements

Decide first whether your length and width are measured along the walls or along the outer eaves. In wall-line mode the calculator adds the overhang on all four sides to get the eave footprint. In eave-to-eave mode the dimensions already include the overhang, so it is not added again. Mixing the two is the most common source of a wrong area, so the measurement basis control is right next to the inputs.

Roof pitch, rise and run

Pitch is the slope of the roof. You can enter it as X/12 (inches of rise per 12 inches of run), in degrees, or from a measured rise and run. All three resolve to one slope ratio. The horizontal distance from the eave to the ridge is the run; the vertical height gained over that run is the rise. A 6/12 pitch rises 6 inches for every 12 inches of horizontal run, which is about 26.57 degrees, not 50 degrees even though it is a 50 percent slope.

Hip Roof Formulas Explained

Surface area and the pitch multiplier

The sloped surface area equals the eave footprint multiplied by the pitch multiplier, which is the square root of (1 + p²) where p is the rise-over-run ratio. So area = Le × We × √(1 + p²). The footprint is the flat area you would measure from above; the multiplier stretches it up the slope. A steeper pitch means a larger multiplier and more material for the same footprint.

Common rafters, hip rafters and the ridge

A common rafter runs straight up the slope from the eave to the ridge, so its line length is the run times √(1 + p²). A hip rafter runs diagonally to the corner, so its plan run is longer by a factor of √2, and its line length is the run times √(2 + p²). A hip is not simply the common length times √2, because both rafters climb the same vertical rise. The ridge length equals the long side minus the short side.

Pyramid roofs and model limits

When the length equals the width the ridge collapses to a single apex and the roof becomes a square pyramid. The four hips and their cap coverage remain; only the ridge line disappears. This model does not handle unequal pitches, L-shaped plans or intersecting roofs. For those, measure the actual sloped faces in the roof area calculator.

Worked Example: 40 × 24 ft at 6/12

Take a 40 by 24 foot building (wall lines), a 6/12 pitch and a 12-inch overhang. The eave footprint becomes 42 by 26 feet. The multiplier is √1.25 ≈ 1.118034, so the area is 42 × 26 × 1.118034 ≈ 1,220.89 sq ft. The ridge is 40 − 24 = 16 ft. The common rafter to the eaves is 13 × 1.118034 ≈ 14.534 ft, and each hip to the eaves is 13 × 1.5 = 19.5 ft. The four hips plus the ridge give 94 linear feet of hip-and-ridge line.

Compare with and without overhang

With a zero overhang the same walls give a 40 by 24 footprint and an area of about 1,073.3 sq ft. Adding the 12-inch overhang raises the footprint to 42 by 26 and the area to about 1,220.9 sq ft. The overhang also lengthens every rafter by its sloping tail, which the calculator reports separately so you can see the eave projection distinctly from the climb up the slope.

Estimate Shingles, Ridge Cap and Waste

Net area vs. order quantity

The net roof area is pure geometry. The order quantity adds a waste allowance for cuts and overlaps: order area = net area × (1 + waste%). Roofing is sold in squares (100 sq ft) and in bundles. Divide the order area by the coverage per bundle and round up. The calculator keeps these as two separate numbers so you never confuse the measured roof with the amount you buy.

Hip and ridge cap coverage

Cap shingles cover the hips and ridge and are a separate line item with their own linear coverage and waste. Add the ridge length to the four hip lengths to get the total cap line, then divide by the coverage per bundle and round up. Coverage printed on a package is the authoritative figure; the default here is a clearly labeled planning example, so check the bundle before ordering.

Methodology and Related Calculators

All results use full internal precision and are rounded only for display. The geometry is verified against independent numeric fixtures described on the methodology page. This tool does not provide cutting dimensions, bevels or structural sizing. Continue with the shingle calculator for bundles, the ridge cap calculator for cap, the hip rafter calculator for diagonal geometry, or the measuring guide.