Roof area from footprint and pitch — plus the eave, rake, ridge and hip lengths that everything at the edges is ordered against.
Roof Area Calculator
Inputs
A 6/12 roof rises 6 inches for every 12 inches of run.
Measured horizontally from the wall. It enlarges the roof in both directions.
Simple gable 10%. Hips and valleys generate cut waste — use 15%.
Results
Roof area
1,502.64 ft²
area = (L + 2×overhang) × (W + 2×overhang) × √(rise² + 144) ÷ 12
Calculated with BuildCalculators.com
Calculated with BuildCalculators.com · buildcalculators.com/roof-area-calculator
Estimates are for planning only — confirm quantities with your supplier or contractor before ordering.
A roof is bigger than the ground it covers, and how much bigger depends only on the pitch. That part is straightforward: multiply the plan area by √(rise² + 144) ÷ 12 and you have the surface. What actually stops people ordering a roof is everything else — the eave, the rake, the ridge, the hips — because gutters, drip edge, ridge cap and hip cap are all sold by the linear foot and none of them come off the area figure.
So this calculator gives you both. Area and squares for the covering, and the four linear dimensions the rest of the job is ordered against, worked out for a gable, a hip or a shed roof.
One result surprises almost everyone: a hip roof has exactly the same surface area as a gable over the same footprint. Every facet sits at the same slope, so both come to the plan area divided by the cosine of the pitch. A hip does not need more shingles. It needs more cutting.
√(rise² + 144) ÷ 12(L + 2×overhang) × (W + 2×overhang) × multiplier2 × width × multiplier(width ÷ 2) × √(288 + rise²) ÷ 12length − widthA sloped surface and its shadow on the ground form a right triangle: 12 units of run, "rise" units of rise, and the slope as the hypotenuse. The ratio of hypotenuse to run is the multiplier, and it applies to every square foot of the roof equally. At 6/12 it is 1.118, so a 1,200 ft² footprint carries 1,342 ft² of roof. At 12/12 it is 1.414 — the square root of two, because the roof is at 45°.
This is worth sitting with, because the intuition says otherwise. Take any footprint and put a uniform pitch on it. Every point of roof surface projects onto exactly one point of the footprint, and every facet is tilted by the same angle, so the total surface is the plan area divided by cos θ regardless of how the planes are arranged. Four hip facets, two gable planes, or a pyramid — same number. What changes is waste: a hip roof has four lines of cut shingles running up its hips and no straight gable ends to run courses out to, so budget 15% rather than 10.
Overhang is measured out from the wall face on the plan, not along the slope. A 12 inch overhang adds a foot at each end and each side, so a 40 × 30 building becomes a 42 × 32 plan — 1,344 ft² instead of 1,200, before the pitch is applied at all. That is a 12% increase from a detail people routinely leave out. Entering the sloped tail length here instead of the horizontal run overstates the roof.
The EAVE is the horizontal bottom edge: gutters, eave drip edge, starter course, and the vents if they are soffit-mounted. On a hip that is the whole perimeter; on a gable it is the two long sides. The RAKE is the sloped gable edge — rake drip edge, and it is longer than the wall it sits above by the pitch multiplier. The RIDGE takes ridge cap and ridge vent. The HIPS take hip cap shingles, and on a hip roof they are frequently longer in total than the ridge.
On a hip roof the ridge is the length minus the width, because the hips run in at 45° from each corner and eat half the width off each end. A 40 × 30 building has a 10 ft ridge. Make it 30 × 30 and the ridge is zero: the four planes meet at a point and you have a pyramid hip, which is all hip cap and no ridge at all.
It handles one roof of one shape. Real houses have dormers, cross-gables, porch roofs at a different pitch and valleys where two sections meet. For those, work out each section separately and add the areas — the arithmetic is the same each time, and valleys get counted like hips for cut waste. If the shapes are irregular enough that this is painful, that is a signal to measure the roof rather than the building.
The most common residential roof there is.
1,503 ft², 84 ft of eave, 71.6 ft of rake, 42 ft of ridge
The overhang added 144 ft² of plan before the pitch touched it. Leaving it out would have under-ordered by more than a square.
Identical footprint, identical 6/12 pitch.
Same area, 148 ft of eave, and 96 ft of hip cap
The area did not move. The eave nearly doubled, the ridge shrank to 10 ft, and 96 ft of hip cap appeared. That is the real difference between the two roofs, and none of it shows up in a square-foot figure.
A lean-to on the back of a garage, 6 in overhang.
233 ft², 2.33 squares
A shed roof has one eave, one high edge and two rakes. At 4/12 the multiplier is only 1.054, so the slope adds barely 5% — which is why low-pitch roofs feel deceptively small and then leak, because the shingles are near their rated limit.
The hip factor is per foot of COMMON run, and matches the framing square tables.
| Pitch | Multiplier | Hip factor | Per ft of run | Angle |
|---|---|---|---|---|
| 3/12 | 1.0308 | 1.4361 | 17.23 in | 14.0° |
| 4/12 | 1.0541 | 1.4530 | 17.44 in | 18.4° |
| 5/12 | 1.0833 | 1.4743 | 17.69 in | 22.6° |
| 6/12 | 1.1180 | 1.5000 | 18.00 in | 26.6° |
| 7/12 | 1.1577 | 1.5298 | 18.36 in | 30.3° |
| 8/12 | 1.2019 | 1.5635 | 18.76 in | 33.7° |
| 10/12 | 1.3017 | 1.6415 | 19.70 in | 39.8° |
| 12/12 | 1.4142 | 1.7321 | 20.78 in | 45.0° |
Area and squares are identical for gable and hip. The rake is gable, the hips are hip.
| Pitch | Roof area | Squares | Rake (gable) | Hips (hip) |
|---|---|---|---|---|
| 4/12 | 1417 ft² | 14.17 | 67.5 ft | 93.0 ft |
| 6/12 | 1503 ft² | 15.03 | 71.6 ft | 96.0 ft |
| 8/12 | 1615 ft² | 16.15 | 76.9 ft | 100.1 ft |
| 10/12 | 1749 ft² | 17.49 | 83.3 ft | 105.1 ft |
| 12/12 | 1901 ft² | 19.01 | 90.5 ft | 110.9 ft |
Area drives the covering and the linear dimensions drive everything at the edges, which is a bigger share of the bill than most people expect. On a typical 15 square roof, drip edge, starter, ridge cap, hip cap and gutters together run $600 to $1,500 — comparable to the shingles themselves at $350 to $700 a square installed.
Drip edge at $2–$4 per linear foot installed, on every eave and every rake. Gutters at $6–$15 per foot. Ridge cap at $3–$6 a foot and hip cap at the same. On the hip version of a 40 × 30 house that is 148 ft of eave and 96 ft of hips — a lot of linear foot to price, and none of it visible in a square count.
Not the material — the area is identical. It is the labour: every course of shingles running into a hip has to be cut on the rake angle, the hip cap has to be laid over it, and there is more edge metal because the eave runs the full perimeter. Expect 10 to 20% more on the installed price for the same square footage.
Above 6/12 a roofer starts moving more slowly; above 8/12 they need staging, roof jacks and harnesses, and above 9/12 most price it as a separate class of work. So steepening a roof raises the bill twice: more area from the multiplier, and a higher rate per square applied to it.
A 6/12 roof is 12% larger than the ground it covers, and a 12/12 roof is 41% larger. Ordering off the footprint under-buys every time, and by more than the waste allowance covers.
It adds twice its width to each plan dimension before the pitch is applied. A 12 inch overhang on a 40 × 30 building is 144 ft² of extra plan — more than a square of roof once the slope is on it.
The plan calculation wants the horizontal run past the wall. Using the sloped tail length inflates every dimension it touches.
It needs the same area and about 50% more waste. Order the same squares, budget 15% waste rather than 10, and add the hip cap — which the area figure never mentions.
Drip edge, gutters, ridge cap and hip cap are all sold by the linear foot. The area figure will not order any of them, and on an edge-heavy roof they are a substantial share of the job.
Dormers, cross-gables and porch roofs at a different pitch each need working separately and adding. Valleys count like hips for cut waste. One rectangle over a complex roof is a guess wearing a decimal point.
Multiply the plan area — including the overhang on all sides — by the pitch multiplier, √(rise² + 144) ÷ 12. A 40 by 30 ft building with a 12 in overhang has a 42 by 32 ft plan, and at 6/12 that is 1,344 × 1.118 = 1,503 ft² of roof.
No — exactly the same, over the same footprint at the same pitch. Every facet sits at the same slope, so both come to the plan area divided by the cosine of the pitch. A hip needs the same squares, about 50% more waste for cutting, and hip cap shingles a gable never needs.
The length minus the width, because the hips run in at 45° from each corner. A 40 by 30 building has a 10 ft ridge. If the building is square the ridge disappears entirely and you have a pyramid hip.
The rake is the sloped gable edge, so it is the building width times the pitch multiplier — and there are two rakes per gable end. On a 32 ft plan width at 6/12 that is 2 × 32 × 1.118 = 71.6 ft of rake in total.
More than people expect, because it adds twice its width to each plan dimension before the pitch is applied. A 12 in overhang on a 40 by 30 building adds 144 ft² of plan — over a square of roof once the slope is on it.
10% on a simple gable, 15% where there are hips or valleys, and more on a cut-up roof with dormers. The waste is cutting, not breakage: every course dying into a hip or valley gets cut on the rake angle.
100 square feet of roof surface. It is the unit roofing is quoted and sold in — a typical 1,500 ft² roof is 15 squares, and a bundle of shingles covers a third of a square.
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This calculator uses published constants from named industry sources, each asserted in an automated test that runs on every build. The formula is printed with the result above, and any correction we make is logged on the changelog.
It is a planning estimate. It does not replace an engineer, a site visit or a written quote — confirm quantities with your supplier before ordering.