What this calculator works out
A roof's true surface area is always bigger than the footprint of the house underneath it, and by more than most people expect. Tilt a flat rectangle up into a slope and the material needed to cover it grows with that tilt, even though the building's footprint on the ground hasn't changed at all. This calculator takes your house's length and width, adds the eaves overhang that every roof has beyond the wall line, and applies your roof's pitch, entered however you already know it, to work out the actual sloped area you need to cover. From there it converts that area into squares, the standard 100 square foot unit roofers order by, and into shingle bundles with a waste allowance for the cuts, edges and off-cuts a real job always produces.
It's built for early budgeting: sizing up a re-roof, comparing shingle costs against a quote, or working out roughly how many bundles to have delivered. It is not a substitute for a roofer's own measurements, and it deliberately leaves out valleys, dormers, skylights and chimney flashing, since those depend on details a footprint alone can't capture.
How the maths works
Start with the plan area, the roof's footprint as seen from directly above, including the eaves overhang on every side. Then apply the pitch multiplier, a single number that converts a flat, horizontal area into the actual sloped surface at a given steepness.
The multiplier comes from simple trigonometry. A roof slope forms the hypotenuse of a right-angled triangle whose two shorter sides are the horizontal run and the vertical rise; the ratio of the sloped length to the flat, horizontal length underneath it is exactly the square root of 1 plus the rise-over-run ratio squared. A flat roof, with no rise at all, has a multiplier of 1, since a level surface's sloped and flat lengths are identical. As the pitch steepens, the multiplier climbs steadily, and it's the same figure whether it's applied to one roof plane or to the whole building's plan area at once.
Working the example through: a 12 by 8 metre house with a 0.3 metre eaves overhang has a plan size of 12.6 by 8.6 metres, which is 108.36 m². A 6:12 pitch is a rise-over-run ratio of 6 ÷ 12, or 0.5, giving a multiplier of √(1 + 0.5²) = √1.25 = 1.118. Multiply the plan area by that multiplier and the actual roof area is 108.36 × 1.118 ≈ 121.15 m², which converts to about 1,304 square feet. Divide by 100 and that's 13.04 squares. At 3 bundles to a square that's 39.12 bundles, rounding up to 40 before waste; add 10% for cuts and the total is 44 bundles to buy.
Rise:run, degrees or percent: three ways to say the same pitch
Roof pitch gets described in three common ways, and they all boil down to the same underlying ratio. The rise:run convention, written as something like "6:12", states the vertical rise for every 12 units of horizontal run, a habit that comes from framing squares marked out in 12ths of a foot. An angle in degrees measures the same slope directly from horizontal, the way a pitch gauge or an inclinometer reads it. A percentage states the rise as a percentage of the run, the convention more common in civil and drainage work than in house framing.
All three describe the 6:12 pitch used above identically: a rise:run ratio of 0.5, an angle of 26.57° (the arctangent of 0.5), and a slope of 50%. Switching between the three in this calculator recalculates the same underlying ratio rather than treating them as separate settings, so the roof area doesn't change just because the pitch was typed in a different way.
Eaves overhang: the size everyone forgets
A house's footprint, measured wall to wall, is smaller than its roof. Every roof extends past the walls at the eaves, commonly by 300 to 600mm (12 to 24 inches), to shed water clear of the walls and give gutters somewhere to sit. Skip that overhang and a roof area estimate quietly comes up short on every single side, not by a small rounding error but by a stripe of real roof running the full length and width of the building. This calculator adds the overhang you enter to both the length and the width before working out the plan area, since it applies at both ends of each dimension, not just one.
Gable and hip roofs: same area, different waste
A gable roof ends in a triangular wall section at each gable end, with the ridge running the building's full length. A hip roof instead slopes inward on every side, with no vertical gable ends and a shorter ridge. It's a reasonable assumption that a hip roof, being more complicated, must cover more actual area than an equivalent gable, but for a single, constant pitch held across the whole roof, that isn't the case. At any point on a roof surface held to one pitch, the ratio of sloped area to the flat plan area directly beneath it is the same multiplier, regardless of whether that point sits on a gable end, a hip face or a plain slope. Add that up across the whole footprint and a hip roof and a gable roof of the same plan size and pitch come out to the same total actual area.
What genuinely differs is how much of that material gets wasted fitting it. A hip roof adds diagonal hip rafters at every corner and often creates valleys where two roof faces meet inward, and both need angled cuts that a plain gable's straight eaves and single ridge simply don't. That's why this calculator keeps a higher waste allowance, typically 15% against a gable's 10%, for hip roofs, valleys or a cut-up roof plan, rather than inventing a different area formula for the shape itself.
Squares and bundles: turning area into material to order
Roofers order material in squares, a trade unit equal to 100 square feet regardless of what's covering it, so a 2,000 sq ft roof is simply "20 squares" in any conversation with a supplier. Standard three-tab and most architectural asphalt shingles are then packaged 3 bundles to a square, meaning 33.3 sq ft of coverage per bundle, though some premium or luxury shingles are heavier and bundled 2 or 2.5 to a square instead. This calculator uses 3 as a typical default and lets that figure be changed to match whatever's printed on your own product.
The bundle count is worked out from the actual roof area, not from a squares figure rounded up first, then a waste allowance is added and the final total rounded up to a whole bundle, since a supplier can't sell part of one. In the worked example, 1,304 sq ft of actual roof area at 3 bundles per square is 39.12 bundles, rounding up to 40 before waste; add 10% for cuts and off-cuts and 40 × 1.10 is 44, with no further rounding needed since that comes out to a whole number already.
A note for UK roofs: tiles, not squares
UK roofing is usually priced and ordered differently. Concrete and clay tiles are sold by coverage per square metre rather than in squares and bundles, and that coverage rate varies a great deal by tile profile, from large-format interlocking tiles that need relatively few per square metre to smaller plain tiles that need several times as many. This page doesn't invent a per-tile coverage figure, because there isn't one general number that's honestly true across tile types; the actual roof area in square metres from the calculation above is the figure to take to a tile manufacturer's own coverage table, or to a merchant, for a tile-specific count.
Measuring your roof safely
The inputs this calculator needs can usually be found without climbing onto the roof at all. Length and width can be measured at ground level with a tape measure along the walls, taken from a property survey or floor plan, or estimated from satellite or aerial imagery. Pitch can be read from the underside of the roof in a loft or attic space, using a level and a tape measure or an angle finder against a rafter, or checked from the ground with a pitch gauge held up against binoculars or a phone camera. Where a closer look genuinely is needed, working from a securely footed ladder without stepping onto the roof surface itself is far safer than walking a sloped, often wet or mossy, surface with no fall protection. Whatever the source of the measurements, treat this calculator's output as a budgeting estimate rather than an order to hand a supplier; a roofer's quote, based on measurements taken on the real building, is the number to build a purchase around.
What this estimate leaves out
This calculator works from a single rectangular footprint held to one pitch, which covers a simple gable or hip roof well but leaves out anything that changes the roof plan itself. Dormers, valleys where two roof sections of different sizes meet, chimneys, skylights and roof penetrations all add cutting, flashing and material beyond a plain footprint calculation, and a roof with several of these features can run well past even the higher 15% waste allowance offered here. Underlayment and roofing nails are needed on every job too; underlayment is typically sold by the roll at a stated coverage per roll, and nail quantity depends on the fastening pattern the shingle manufacturer specifies, so neither gets an invented figure on this page. Both are worth pricing from the shingle manufacturer's own installation instructions once the roof area above is settled.
Questions people ask
Why does a steeper roof need more material for the same house?
Because the material has to cover the sloped surface, not the flat footprint underneath it. Tilting a surface up increases its true surface area even though the building's footprint on the ground stays exactly the same, and the pitch multiplier is simply how much bigger that sloped surface is.
How do I convert between rise:run, degrees and percent pitch?
All three reduce to the same rise-over-run ratio. Rise:run divides rise by run directly (run is 12 in "X:12" notation); degrees convert with the tangent function, ratio = tan(angle); percent is just that ratio times 100. A 6:12 pitch, a 26.57° angle and a 50% slope are the same pitch described three ways.
Why does the eaves overhang matter so much?
Because a roof always extends past the walls, typically 300 to 600mm, on every side. Leaving it out under-measures the plan area on all four edges of the building at once, which is a bigger shortfall than it looks like from a single small measurement.
Do hip roofs really need more material than gable roofs?
Not in total area, if the pitch is the same throughout: a constant-pitch roof surface always covers plan area times the same multiplier, whatever shape it's cut into. What a hip roof does need more of is waste, since its hip rafters and valleys create more angled cuts, which is why this calculator uses a higher waste allowance for hips rather than a different area formula.
How many shingle bundles are in a square, and does that change?
Standard three-tab and most architectural shingles are packaged 3 bundles to a square (100 sq ft), but it isn't universal; some premium or luxury shingles are bundled 2 or 2.5 to a square because the shingles themselves are heavier. Check the number printed on your chosen product and change the bundles-per-square figure here to match it.
Can I use this for a UK roof with concrete or clay tiles?
The area, squares and pitch working are all still valid for a UK roof. The bundle figure is specific to shingles, though; tiles are sold by coverage per square metre and that rate varies a lot by tile profile, so take the calculated roof area in square metres to your tile manufacturer's own coverage table instead.
Is this accurate enough to order materials directly from?
Treat it as a budgeting estimate. It leaves out valleys, dormers, skylights and chimney flashing, and it relies on the footprint and pitch you enter being accurate. A roofer's quote, built from measurements taken on the actual roof, is the number to order material against.
This calculator uses the standard roofing-trade pitch multiplier (the square root of 1 plus the rise-over-run ratio squared) to convert a plan footprint into actual roof area, and common trade waste allowances for gable and hip or valley roofs. Shingle bundle counts are typical for standard shingles; check your own product's packaging, since some premium shingles bundle differently. This is an estimate for budgeting, not a substitute for a roofer's own measurements and quote.