Roof Pitch Calculator – Pitch, Angle and Rafter Length

Your roof, drawn to scale

The triangle below is your roof’s cross-section, redrawn from your own numbers every time they change. The sloped side is the rafter; the angle at the eave is the pitch angle.

Common roof pitches

Every standard pitch from 1/12 to 12/12, worked out from the same formulas this calculator uses. The row for 6/12 — this page’s starting example — is highlighted.

Pairs well with this calculation

The angle underneath the pitch, the slope as its own tool, and the triangle the rafter lives in.

Roof pitch in three steps

How the roof pitch calculator works

Going deeper

Three roofs, one triangle: the pitch ladder

Every row below was run through this page’s own calculator. The first two rows are the page’s own worked examples; the third is a single-input change from the default, verified on the page.

The second row is the one that teaches the method. A level held in the attic shows a rise of 8 inches over a run of 24 inches: pitch is 8 ÷ 24 × 12 = 4, a 4/12 roof, and the angle is atan(8 ÷ 24) = 18.43°. The run being 24 rather than 12 changes nothing — the ratio is what carries the steepness, and scaling the ratio to 12 is what the pitch figure does. The rafter per 12 of run for a 4/12 roof is √(12² + 4²) = √160 = 12.65, a multiplier of 1.054 — the number roofs are actually ordered by, since it turns a run length into a rafter length by multiplication. The third row shows what happens when the rise grows on the same run: 8 over 12 is an 8/12 pitch, 33.69°, a 66.67% slope, and a rafter of √(64 + 144) = √208 = 14.42 per 12 of run, multiplier 1.202. Steeper roof, longer rafter, larger multiplier — all three readings moving together, because all three are the same triangle.

The whole-roof example on this page shows why the multiplier matters more than the pitch for ordering. A house 40 feet wide has a run of 20 feet from eave to ridge; at 6/12 the rise is half the run, 10 feet, and the rafter is √(100 + 400) = √500 = 22.36 feet — before any overhang is added at the eave. The multiplier gives the same answer faster: 20 feet of run × 1.118 = 22.36 feet of rafter. Overhang is then added on top, not inside the triangle: the rafter length the page returns is the slope length over the run you typed, and the eave overhang extends it beyond the wall. Forgetting the overhang under-orders; including it inside the run over-steepens the pitch. Keep the two separate — run to the ridge for the triangle, overhang added after — and the numbers stay honest.

Pitch, slope and angle: three languages, one steepness — do not mix them

North American carpenters quote pitch — rise per 12 of run — because a framing square is built around it and because 12 divides neatly by 2, 3, 4 and 6. Engineers and road builders quote slope percent instead: the same ratio times 100, so a 6/12 pitch is a 50 percent slope. And anyone with a protractor, a phone inclinometer or a trigonometry habit quotes the angle in degrees: 26.57° for that same 6/12 roof. All three describe the identical triangle, and confusing them is expensive. A “50 percent roof” and a “50 degree roof” are wildly different objects — 50 percent is 26.57°, while 50° is a pitch of about 14.3/12, ski-slope territory for a house. A 100 percent slope is not vertical; it is 45°, a 12/12 pitch. Vertical would be an infinite slope, because the run would be zero and the ratio would divide by nothing. When a figure is quoted without its language, ask which one is speaking before you cut anything — and when you quote one yourself, name the language with the number.

Converting between the languages runs through the tangent both ways, and the page’s own example shows it. A design that calls for a 30° roof has a tangent of 0.577, and 0.577 × 12 = 6.93 — so a 30° roof is a pitch of about 6.9/12, which a builder would round to a 7/12. Going the other way, a 7/12 pitch has a ratio of 7 ÷ 12 = 0.583, and atan(0.583) = 30.26° — close to 30°, but not exactly, because the rounding to a whole pitch number moved the angle by about a quarter of a degree. That quarter-degree is the cost of rounding to a builder-friendly pitch, and it is usually harmless — but if a design dimension depends on the exact angle, work from the angle, not from the rounded pitch. Everything on this page is computed at full precision and rounded only for display (angle to two decimals, rafter to two, multiplier to three, pitch per 12 with up to two decimals), so a rise of 7.5 over a run of 29 honestly reads 3.1/12 rather than being forced to a whole number — and that honesty is worth preserving in your own notes rather than rounding it away a second time.

Measuring the roof you have, and choosing the roof you want

The classic measurement needs no ladder: a 12-inch level held against the roof from inside the attic, reading the vertical drop at its end, gives the rise per 12 directly. That reading is the pitch with no arithmetic at all — if the level reads 6 inches, the roof is 6/12. If the attic is inaccessible or the roof is already sheeted, measure any stretch instead: rise over any run, and the page scales it to 12 for you, as the 8-over-24 example shows. The measurement errors to avoid are the obvious ones, stated plainly: measuring along the slope instead of horizontally for the run (which understates the pitch, because the slope length is longer than the run), and measuring the rise to the wrong point (the top of the roofing instead of the top of the rafter, or vice versa). A pitch measured from the wrong points is a pitch for a different roof, and every number downstream — angle, slope, rafter, multiplier — inherits the error exactly.

Choosing a pitch, rather than measuring one, is a different decision with its own trade-offs, and the page’s own band guidance frames it: the conventional band — steep enough for standard asphalt shingles and most common roofing materials, with a healthy margin for shedding water and snow, and comfortable to work on with care — is where most house roofs live, and the 6/12 default sits in it. Shallower roofs shed water more slowly and demand more careful waterproofing at every joint; steeper roofs shed faster but cost more in materials (the multiplier again — a 12/12 roof needs 1.414 feet of rafter per foot of run, against 1.118 for 6/12) and are harder and more dangerous to work on. The pitch is therefore never just a shape: it is a materials quantity, a waterproofing decision and a safety decision, all read off one triangle.

The common pitches, side by side

Every row below was run through this page’s own calculator at a run of 12, so the pitch, angle, slope, rafter and multiplier all describe the same triangle at five standard steepnesses.

Read the multiplier column from top to bottom and the cost of steepness becomes concrete. A 4/12 roof needs 1.054 feet of rafter per foot of run; a 12/12 roof needs 1.414 — about a third more timber for the same run, before overhang, before waste, before the steeper roof’s harder working conditions. The angle column tells the same story in degrees: 18.43° at the shallow end against 45.00° at the steep end, with the conventional band — the 6/12 default at 26.57° and its neighbours — sitting in the middle where standard materials, water shedding and safe working meet. The slope column is the one to quote to engineers and road builders: 33.33% for 4/12, 50% for 6/12, 100% for 12/12 — and the 12/12 row is the standing correction to the commonest slope misconception, because 100% slope is 45°, not vertical. Vertical would be an infinite slope, a run of zero, a ratio dividing by nothing.

Below the table’s shallow end, the same formulas keep working all the way to flat. A 2/12 pitch has an angle of atan(2 ÷ 12) = 9.46° and a slope of 16.67%, with a rafter of √(144 + 4) = √148 = 12.17 per 12 of run, multiplier 1.014. A 1/12 pitch is 4.76° and 8.33%, rafter √145 = 12.04, multiplier 1.003. And a perfectly flat roof — 0/12 — is 0°, 0% slope, rafter exactly 12.00 per 12 of run, multiplier exactly 1.000: the rafter is the run, because there is no rise to lengthen it. The progression is smooth and unbroken from flat to steep, which is the point: pitch is a continuous ratio, not a set of named bands, and any rise over any run — including rises the table does not list — has an angle, a slope, a rafter and a multiplier given by the same three formulas. The named pitches in the table are the common ones, not the only ones, and a roof at 3.1/12 (the page’s own example of an honestly displayed non-whole pitch, from a rise of 7.5 over a run of 29) is exactly as calculable as a roof at 6/12.

Two rows in the table are exact in a way the others are not, and they are worth noticing because exactness is rare in construction. The 9/12 row is a 3-4-5 triangle scaled by three: rise 9, run 12, rafter 15 exactly, multiplier exactly 1.250, angle 36.87° — the only row where the rafter comes out whole. The 12/12 row is a 45° right triangle: rafter √288 = 16.97, multiplier √2 = 1.414, slope exactly 100%. The 5/12 row is exact in a different way: rise 5, run 12, rafter √(25 + 144) = √169 = 13.00 exactly — another Pythagorean triple, 5-12-13, hiding in a roof table. When a pitch gives a whole-number rafter, setting out gets easier and cutting lists get cleaner; when it does not, the page’s two-decimal rafter is the figure to cut to, and the multiplier’s three decimals are the figure to order by. Either way, the triangle does not negotiate: the rafter is the square root of rise squared plus run squared, whatever the pitch, and every row in the table is that one formula, six times.

The pitch ladder: angle and multiplier from 3/12 to 12/12

Pitch is rise over a 12-inch run. The multiplier is what you order by.

Roof pitch is stated as rise over a 12-inch horizontal run, and two numbers follow from it: the angle and the multiplier. A 3/12 pitch rises 3 inches per foot of run, sits at 14.04°, and multiplies the run by 1.0308 to give the rafter length. A 5/12 pitch is 22.62° with a 1.0833 multiplier; 7/12 is 30.26° at 1.1577; 10/12 is 39.81° at 1.3017; and 12/12 — a 45° roof — multiplies by 1.4142, the square root of 2. The rafter is always the square root of rise squared plus run squared, whatever the pitch, and every row of the ladder is that one formula, six times.

The multiplier matters more than the pitch for ordering, because timber, sheathing and roofing are all measured along the slope, not along the plan. A 20 ft run at 6/12 needs a 22.36 ft rafter (20 × 1.1180); the same run at 12/12 needs 28.28 ft (20 × 1.4142) — six extra feet of timber per rafter for the same footprint. For a 30 × 40 ft gable at 6/12, the 15 ft half-span gives a 16.77 ft rafter and 1,341.64 sq ft of roof area. Order from the multiplier, not from the plan dimensions: the plan is the shadow, and the roof is the thing casting it.

Angles, multipliers, rafters and roof area: roof pitch explained.

Measuring a real roof: rise, run, and the ridge you cannot reach

Measure the run from the outside of the wall to the ridge line, and the rise where you can reach it.

The run is the horizontal distance from the outside face of the wall to the centre line of the ridge — not to the eave, and not to the fascia. The rise is the vertical distance from the wall plate to the ridge. Where the ridge cannot be reached, measure the rise over a known run instead: a 4 ft level held horizontally from the roof surface, with the vertical drop measured at its end, gives rise over 4 ft of run, and dividing by 4 gives the pitch per foot. A 16-inch drop over 4 ft is a 4/12 pitch — the same ratio, measured where hands can reach.

Two cautions belong with every measurement. First, hips and valleys change the geometry: the common rafters follow the ladder above, but hip and valley rafters run diagonally and are longer, and the calculator’s figures are for the common rafter and the roof area, not for the hips. Second, waste and overlap belong in the order, not in the measurement: sheathing, felt and shingles all need their laps and cuts added after the area is computed, at the supplier’s stated allowances. Measure the roof; order the roof plus its allowances.

Frequently asked questions

Related calculators

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