Quick answer
A 6/12 roof rises 6 inches for every 12 inches of horizontal run: that is an angle of 26.57° (the arctangent of 6 ÷ 12), a 50% slope, and 1.118 feet of rafter or roof surface for every foot of run. The angle comes from trigonometry alone; which roof coverings a pitch allows is set by the building code (IRC 2021 Chapter 9).
About the Roof Pitch Calculator
This calculator turns a roof's slope — measured as rise over run or read off as an angle — into the numbers framers, roofers and estimators reach for next: the x/12 pitch, degrees, percent grade, the pitch multiplier and the hip/valley factor. Give it the building's span and length and it carries on to the common rafter length, ridge height, sloped roof area, roofing squares and shingle bundles. It also checks the pitch against the minimum slopes the 2021 International Residential Code sets for common roofing materials, so you know straight away whether shingles, tile or slate are even an option.
How to use it
Pick how you know the slope. If you measured it with a level and a tape, choose Rise & run and enter how many inches the roof climbs over a level distance — the classic method is 12 inches of run, which gives the pitch directly as "x in 12". If you have an angle from a plans set, an angle finder or a phone app, choose Angle. Every other number updates as you type.
The Roof size fields are optional. Give the building width (the span from outside wall to outside wall) and you get the ridge height and the length of a common rafter. Add the building length and the calculator works out the sloped roof area, roofing squares and how many bundles of shingles to order. Lengths accept decimals or feet-and-inches such as 30' 6".
Below the results, Show the math lists every step with your numbers substituted, so you can check the arithmetic, copy it into an estimate, or explain it to a customer. The Copy link button saves the exact inputs in the address, which is handy for sending a takeoff to a crew lead.
Use cases
- Ordering shingles for a re-roof. Enter the footprint and overhang to get squares and bundles with a waste allowance, instead of guessing from the ground.
- Checking a low porch or addition roof. See whether the slope clears the 2/12 asphalt-shingle minimum and whether double underlayment is required below 4/12.
- Laying out rafters for a shed or garage. Span, pitch and ridge board thickness give the line length of a common rafter before plumb and seat cuts.
- Translating plans or a phone reading. Turn an angle in degrees into the x/12 pitch that suppliers, inspectors and installation guides use.
- Comparing design options. Try two pitches on the same footprint to see how much extra surface — and material — a steeper roof adds.
How roof pitch is calculated
Pitch is a ratio: vertical rise divided by horizontal run. Roofers in the US quote it per 12 inches of run, so a roof that rises 6 inches for every 12 inches across is a 6/12 (said "six in twelve"). Everything else on this page comes from that one ratio:
pitch = rise ÷ run × 12
angle = atan(rise ÷ run)
slope % = rise ÷ run × 100
multiplier = √(1 + (rise ÷ run)²)
The pitch multiplier (also called the slope factor) converts a level measurement into the true length along the roof. A 6/12 roof has a multiplier of 1.118, which means every foot measured level on the plan becomes 1.118 feet on the slope. Multiply a footprint area by the same factor and you get the sloped area — and that holds for hip roofs as well as gables, as long as every plane has the same pitch.
For hips and valleys we also show the hip/valley factor, √(pitch² + 16.97²) ÷ 12. A regular hip runs diagonally across the corner, so for every 12 inches of common run it covers 16.97 inches of level distance; the factor turns that into length along the hip rafter.
Worked example: a 30 × 40 ft gable at 6/12
The house is 30 ft wide and 40 ft long, with 12-inch overhangs and a 2× ridge board (1½ inches thick). The roof rises 6 inches per foot.
- Ratio = 6 ÷ 12 = 0.5, so the angle is atan(0.5) = 26.57° and the slope is 50%.
- Multiplier = √(1 + 0.5²) = 1.1180.
- Ridge height = half the span × ratio = 15 × 0.5 = 7.5 ft above the wall plate.
- Common rafter (line length) = (15 ft − ¾″ for half the ridge + 1 ft overhang) × 1.1180 ≈ 17.82 ft. Cut length still needs the plumb cut and birdsmouth, which depend on your lumber and seat cut.
- Plan area including overhangs = 32 × 42 = 1,344 sq ft; sloped area = 1,344 × 1.1180 ≈ 1,503 sq ft, or 15.03 squares.
- With 10% waste that is 16.53 squares; at 3 bundles per square, order 50 bundles.
Roof pitch chart
The most common residential pitches, with the numbers framers and estimators reach for. The full pitch-to-degrees chart runs from ¼/12 to 24/12 and includes the reverse lookup from degrees.
| Pitch | Angle | Slope | Multiplier | Hip/valley |
|---|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1.003 | 1.417 |
| 2/12 | 9.46° | 16.7% | 1.014 | 1.424 |
| 3/12 | 14.04° | 25% | 1.031 | 1.436 |
| 4/12 | 18.43° | 33.3% | 1.054 | 1.453 |
| 5/12 | 22.62° | 41.7% | 1.083 | 1.474 |
| 6/12 | 26.57° | 50% | 1.118 | 1.500 |
| 7/12 | 30.26° | 58.3% | 1.158 | 1.530 |
| 8/12 | 33.69° | 66.7% | 1.202 | 1.563 |
| 9/12 | 36.87° | 75% | 1.250 | 1.601 |
| 10/12 | 39.81° | 83.3% | 1.302 | 1.641 |
| 11/12 | 42.51° | 91.7% | 1.357 | 1.685 |
| 12/12 | 45.00° | 100% | 1.414 | 1.732 |
Which roofing materials work at your pitch
Pitch decides what you are allowed to put on the roof. The International Residential Code (2021 edition, Chapter 9) sets minimum slopes: asphalt shingles need at least 2/12, and between 2/12 and 4/12 they must go over a double layer of underlayment. Clay and concrete tile start at 2½/12, metal shingles and wood shingles or shakes at 3/12, and slate at 4/12. Standing-seam metal panels can go as low as ¼/12. The calculator checks your pitch against each of these and flags anything that is too low. Your local code and the manufacturer's installation instructions can be stricter, and the manufacturer's warranty usually depends on following them.
The trade also uses looser names. The roofing industry treats 3/12 and below as low slope (membranes, modified bitumen, some metal) and anything steeper as steep slope. Most homes fall between 4/12 and 9/12; above about 9/12 crews start to need roof jacks or staging, and above 12/12 (45°) labor costs rise noticeably.
How to measure the pitch of an existing roof
From the roof: hold a 2-foot level flat against the shingles with one end touching, mark 12 inches along the level, and measure straight down from that mark to the roof surface. That vertical distance is the rise per 12. From the attic: do the same against the underside of a rafter, which avoids walking on the roof. From the gable end: measure the overall rise from the top plate to the ridge and divide by half the span. Phone angle apps work too — enter the angle in degrees and the calculator converts it.
Limits of this calculator
- Roof area assumes every plane shares one pitch. For roofs with mixed pitches, dormers or porches, calculate each section separately and add them up.
- Rafter length is the theoretical line length. It deducts half the ridge thickness and includes the overhang, but not the plumb-cut geometry, birdsmouth depth or fascia board.
- Shingle counts assume 3 bundles per 100 sq ft. Some architectural shingles cover slightly less per bundle; starter strip and ridge cap are usually ordered separately — check the wrapper.
- It does not size rafters, check snow or wind loads, or replace engineered truss drawings.
Worked examples
| Pitch | Angle | Slope | Multiplier |
|---|---|---|---|
| 3/12 | 14.04° | 25.0% | 1.031 |
| 4/12 | 18.43° | 33.3% | 1.054 |
| 5/12 | 22.62° | 41.7% | 1.083 |
| 6/12 | 26.57° | 50.0% | 1.118 |
| 8/12 | 33.69° | 66.7% | 1.202 |
| 10/12 | 39.81° | 83.3% | 1.302 |
| 12/12 | 45.00° | 100.0% | 1.414 |
Sources
Frequently asked questions
What is the most common roof pitch?
Most US houses are built between 4/12 and 9/12, with 6/12 (26.57°) the single most common. It sheds water and snow well, can be walked on carefully, and takes standard asphalt shingles with ordinary underlayment.
How do I convert roof pitch to degrees?
Divide the rise by 12 and take the arctangent: angle = atan(pitch ÷ 12). A 4/12 roof is 18.43°, 6/12 is 26.57°, 8/12 is 33.69° and 12/12 is exactly 45°. Choose the Angle mode above to go the other way.
What is a pitch multiplier used for?
It converts level (plan) measurements into lengths and areas along the slope. Multiply the footprint area, including overhangs, by the multiplier to get the roof surface area; multiply a level run by it to get a rafter's line length.
How many bundles of shingles are in a square?
A roofing square is 100 square feet, and most standard three-tab and architectural shingles come three bundles to the square. Check the coverage printed on the bundle — some products cover a little less than 33⅓ sq ft each.
How much waste should I add for shingles?
Around 10% for a simple gable roof and 15% for a hip roof or one with valleys, dormers and lots of cuts. Very cut-up roofs can need more. Enter your own figure in the Shingle waste field.
What is the minimum pitch for asphalt shingles?
Under the 2021 International Residential Code, asphalt shingles need a slope of at least 2/12, and roofs from 2/12 up to 4/12 require double underlayment. Below 2/12, use a low-slope membrane or a metal system rated for the slope.
Is roof pitch the same as roof slope?
People use the words interchangeably. Strictly, pitch is often quoted as rise per 12 inches of run (6/12) while slope can be written as a percentage (50%) or a ratio. The calculator shows all three so you can match whatever your plans or supplier use.
Disclaimer. Results are estimates for planning and ordering. They are not engineering, do not size framing members, and do not replace your local building code, the manufacturer's installation instructions or a licensed contractor's measurements.
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