Stepwise.

Roof Pitch Calculator

Convert roof pitch between rise per 12, degrees and percent grade, and get rafter lengths, the true roof area from a footprint, and the minimum pitch each covering needs.

How to use this calculator

  1. 1To measure an existing pitch from inside the attic, hold a level horizontally against a rafter, mark 12 inches along it, and measure straight up to the rafter from that mark. That measurement is the rise.
  2. 2Use the building span for the roof outputs - the calculator halves it to get the rafter run on a simple gable.
  3. 3Order roofing material from the roof area rather than the footprint. At a 6/12 pitch that is 12% more.
  4. 4Check the minimum pitch table before choosing a covering. It is the part of a roof design that actually goes wrong.

How the calculation works

Angle = arctan(rise / 12) Percent grade = rise / 12 x 100 Slope factor = sqrt(rise^2 + 144) / 12 Hip and valley factor = sqrt(rise^2 + 288) / 12 Roof area = plan area x slope factor
rise
Vertical rise in inches over a 12 inch horizontal run - the first number in "6/12"
Slope factor
Rafter length divided by its run. Multiply a footprint by it to get the real roof surface
Hip factor
The same idea on the diagonal. The 288 is 12 squared twice over, because a hip runs at 45 degrees in plan

Pitch is always expressed over a 12 inch run in the United States, which is why it looks like a fraction and behaves like a tangent. In much of the world the same thing is quoted in degrees or as a ratio of rise to span.

Slope factor and hip factor differ because a common rafter runs straight up the slope while a hip runs up the diagonal of a square. Framing squares carry both scales for exactly this reason.

Roof area from plan area assumes a simple roof. Dormers, crickets and changes of pitch each need their own calculation, and complex roofs are usually taken off plane by plane.

Worked example

The common 6/12 roof

  1. 1.6/12 is arctan(6/12) = 26.57 degrees, and a 50% grade.
  2. 2.The slope factor is sqrt(36 + 144)/12 = sqrt(180)/12 = 1.1180.
  3. 3.A 28 ft wide building has a 14 ft rafter run, so the common rafter is 14 x 1.1180 = 15.65 ft to the wall, plus the overhang.
  4. 4.The footprint including overhangs is 30.67 by 42.67 ft = 1,309 sq ft, and the roof surface is 1,463 sq ft - 154 sq ft more, which is a square and a half of shingles.

Result: 26.57 degrees, slope factor 1.118, 1,463 sq ft of roof

Measuring a pitch from the attic

  1. 1.A level held against a rafter, marked at 12 inches, with 9 inches measured straight up to the rafter from that mark.
  2. 2.Rise 9 over run 12 is a 9/12 pitch directly - the measurement is already in the units pitch is quoted in.
  3. 3.That is 36.87 degrees, a 75% grade, and a slope factor of 1.25.
  4. 4.At 9/12 the roof is steep enough to need fall protection to work on, and the roof surface is a full quarter larger than the footprint.

Result: 9/12 - 36.87 degrees and a slope factor of exactly 1.25

A low-slope addition where shingles do not belong

  1. 1.1.5/12 is 7.13 degrees and a 12.5% grade - the kind of pitch a shed dormer or a back-porch addition ends up with.
  2. 2.The slope factor is only 1.0078, so the roof is barely larger than its footprint.
  3. 3.But it is below 2/12, and below 2/12 asphalt shingles are not a permitted roof covering at any underlayment specification.
  4. 4.Water sits long enough on a slope this shallow for wind to drive it back up under the laps. It needs a membrane, and the number of these roofs shingled anyway is why low-slope additions leak.

Result: 1.5/12 - too shallow for shingles at any specification

Why roofs are described over twelve

A pitch of 6/12 means the roof rises six inches for every twelve inches it travels horizontally. The twelve is arbitrary and universal, and it survives because a framing square has a twelve inch blade - the carpenter lays the square on the rafter stock, reads twelve on one leg and the rise on the other, and marks the cut without calculating anything.

That is also why the number behaves like a tangent rather than like an angle. A 12/12 roof is 45 degrees, and a 24/12 roof is not 90 degrees but 63.4. Doubling the pitch does not double the angle, which catches people out when they try to interpolate.

The rest of the world mostly uses degrees, or the rise as a fraction of the span. Converting is straightforward but the conventions differ in an important way: pitch in the American sense is rise over *run*, which is half the span on a gable, and "pitch" in some older British usage is rise over the full span. A 6/12 American roof and a 1-in-4 British pitch describe the same roof.

The slope factor, and the shingles nobody ordered

Every takeoff starts from a plan area - a footprint measured from a drawing, off a satellite image, or by walking round the building with a tape. A roof surface is always larger than that, by the ratio of the rafter length to its run, and that ratio is the slope factor.

At 4/12 it is 1.054, so 5% more material. At 6/12 it is 1.118, or 12%. At 9/12 it is 1.25, and at 12/12 it is the square root of two - a 41% increase. Those are not trivial fractions on a roof of any size, and ordering from a footprint is the classic way to end up a square short on a Friday afternoon.

The factor applies to anything measured over the roof surface: shingles, underlayment, sheathing, ice-and-water shield, labour. It does not apply to anything that falls vertically or is measured in plan - snow load, rainfall, and the length of the ridge all work on the footprint.

  • 3/12 — Slope factor 1.031. Low, walkable, and near the limit for standard shingles.
  • 4/12 — 1.054. The most common minimum for ordinary shingle work.
  • 6/12 — 1.118. The default residential pitch across much of the country.
  • 9/12 — 1.250. Steep - fall protection territory, and a quarter more material.
  • 12/12 — 1.414. Forty-one percent more surface than footprint.

Minimum pitch is where roofs actually fail

Asphalt shingles are not a waterproof membrane. They are overlapping scales that shed running water, and they depend on that water leaving fast enough that wind cannot drive it back up under the laps. That mechanism has a slope below which it stops working.

The model code puts the floor for asphalt shingles at 2/12, and requires a doubled underlayment between 2/12 and 4/12 precisely because the shingles alone are not trusted in that band - the second layer of underlayment is doing the real waterproofing. Below 2/12, shingles are not a permitted covering at all.

A great many low-slope porch roofs, shed dormers and rear additions are shingled anyway, because they are attached to a shingled house and matching seemed obvious. Those are the roofs that leak at the wall junction every few years and get patched rather than corrected. The right answer on a genuinely low slope is a membrane, and it looks different, and it works.

What this assumes, and where it stops

Assumptions

  • Rafter lengths are measured along the top edge from the outside face of the wall to the centre of the ridge, before any allowance for ridge thickness or cut geometry.
  • The roof is a simple gable or hip of a single pitch. Dormers, crickets and pitch changes need their own takeoff.
  • Roof area includes the overhang all round, which is how roofing is actually measured.
  • Minimum pitches follow the model residential code. Manufacturers sometimes permit lower slopes for specific systems and local amendments vary.

Limitations

  • It does not size rafters. Whether a rafter of a given length and spacing can carry the load is a span table or an engineering question, and it depends on species, grade, spacing and load.
  • Complex roofs with several planes, dormers and valleys need a plane-by-plane takeoff. A single slope factor over a whole footprint under-counts them.
  • Cut geometry - plumb cuts, birdsmouths, ridge thickness, tail cuts - is not included in the rafter length.
  • Waste allowances vary widely with roof complexity. Ten percent suits a simple gable; a cut-up roof with several valleys can need twenty or more.

Common questions

How do I measure the pitch of my roof?

From inside the attic, which is safest. Hold a spirit level horizontally with one end against the underside of a rafter, mark twelve inches along the level, and measure vertically from that mark up to the rafter. That measurement is the rise, and the pitch is that rise over 12. From outside, a pitch gauge held against a rake board does the same thing.

What is the difference between pitch and slope?

In American practice they are used interchangeably and both mean rise over a twelve inch run. Strictly, slope is rise over run and pitch is rise over span - which is half of it - so an older text describing a "quarter pitch" roof means what a roofer today would call 6/12. Where it matters, check whether the denominator is the run or the whole span.

What is the minimum pitch for shingles?

Two in twelve, and only with a doubled underlayment up to four in twelve. Above four in twelve is standard installation with a single layer. Below two in twelve asphalt shingles are not a permitted roof covering, and the correct answer is a single-ply membrane, modified bitumen, or a metal system rated for low slope.

Why is my roof area bigger than my house footprint?

Because the roof is sloped and the footprint is not. The ratio between them is the slope factor - 1.118 at 6/12, meaning 12% more surface than plan. It is the reason material orders based on a footprint come up short, and it is worth applying to everything measured over the roof: shingles, underlayment, sheathing and labour.

What pitch can I walk on?

Up to about 6/12 in dry conditions with sensible footwear, which is why so many houses are built in that range - it can be maintained without staging. From 7/12 upwards roof jacks or a harness are needed, and above 9/12 most roofers price the work differently. Wet, mossy or frosted roofs are a different question at any pitch.

Sources

Formula and content last reviewed on .

Results are estimates for information only, not professional advice.

Report an error

Related calculators

Tools people commonly use alongside the roof pitch calculator.

See all science & engineering calculators →