Roof Pitch Calculator - Angle, Rafter Length & Multiplier

How to use it

1. Pick the solve mode that matches what you know. Measured 5 in of rise against a 12 in level in the attic? Use rise and run. Reading a plan that says 6/12? Use the ratio. Setting a saw from a protractor app? Use the angle. Only know the ridge height and the building width? Use rise and span, and the tool halves the span for the run.
2. Or tap a preset: 2/12 for a shed or porch (the low-slope rules kick in), 4/12 for a ranch or garage, 6/12 for the most common roof, 8/12 or 9/12 for steeper traditional lines, 12/12 for a colonial at a full 45 degrees.
3. Read the slip: the pitch in x/12 to the nearest sixteenth, the angle to a tenth of a degree, the percent slope, and the pitch multiplier to four decimals. The classical pitch fraction (rise over span, the old-book style) sits underneath as a labeled footnote so the two systems never get confused.
4. Check the category chip. Low slope, conventional, or steep tells you at a glance what the roof means for materials and for walking on it, with an honest note about roof jacks and staging where they apply.
5. Turn on the rafter takeoff and enter the building span, the ridge board (1.5 in for a 2x ridge, none for trusses), and the overhang projection. You get the rafter line length after the ridge deduction, the tail, the total, and the stock board to buy rounded up to 8 through 20 ft lumber.
6. Add the roof length and spacing (16 or 24 in on center) for the rafter count on both sides, and a price per board if you want the order costed.
7. Open the quick area check to multiply a footprint by the pitch multiplier: roof surface, squares, and a rough bundle count with 10 percent waste. It is a sanity check, not a shingle order; the full takeoff belongs in a roofing calculator.
8. Scan the material minimums panel: for your computed pitch, each common covering shows whether it is allowed under the IRC minimum slopes, including the asphalt double-underlayment band from 2:12 to under 4:12.
9. Print the pitch chart at the bottom when you want the whole 1/12 to 18/12 conversion table on paper in the truck.

At a glance

• 5 in of rise on a 12 in level in the attic: A 5/12 roof: 22.6 degrees, 41.7 percent slope, multiplier 1.0833. Conventional and generally walkable with care.
• 24 ft span at 6/12 with a 2x ridge and 12 in overhang: Effective run 143 1/4 in, rafter line length 13 ft 4 3/16 in, tail 13 7/16 in, total about 14 ft 5 9/16 in: buy 16 ft stock.
• A 30 degree roof, converted for the plans: 6.93/12, so call it 7/12 on site: 57.7 percent slope, multiplier 1.1547.

How the math works

Everything is one right triangle. The slope is the rise divided by the run, and the pitch in x/12 is that slope times 12, because American roofing states rise per 12 inches of run. The angle is the arctangent of rise over run; for a ratio the tool computes atan(x/12), and for an angle it goes the other way with the tangent. Percent slope is rise over run times 100. The pitch multiplier is the hypotenuse of the triangle divided by the run, which works out to the square root of 1 plus the slope squared: multiply any horizontal footprint length or area by it to get the true length or area along the slope. The classic anchors fall straight out of the math: 4/12 gives 1.0541, 6/12 gives 1.1180, 9/12 gives exactly 1.25 (the 9-12-15 triangle), and 12/12 gives 1.4142, the square root of two. For rafters the tool takes half the building span as the run, deducts half the ridge board thickness, and multiplies that effective run by the multiplier for the line length, measured along the rafter from the ridge plumb cut to the birdsmouth plumb line. The tail is the overhang's horizontal projection times the same multiplier, the total is line plus tail, and the stock board is that total rounded up to the next standard length from 8 to 20 ft. The rafter count is floor(roof length in inches divided by spacing) plus one per side, times two sides. The quick area check multiplies the footprint by the multiplier for the surface, divides by 100 for squares, and figures three bundles per square plus 10 percent waste. The classical pitch footnote divides the total rise by the total span instead of the run, which is why an old book calls a 6/12 roof a quarter pitch.

1. 1. Start from what you can measure

   Pick the input you trust. In an attic, hold a level horizontal against the underside of a rafter, mark 12 in along it, and measure straight down to the rafter at the mark: that vertical distance is the rise per 12 in of run, which IS the pitch. Say you measure 6 in: that is a 6/12 roof, no conversion needed. From plans, take the ratio directly. From a smartphone inclinometer laid on the rake board, take the angle. If all you have is a tape from outside, measure the ridge height above the top plate and the building width: rise and span mode halves the span for the run.

2. 2. Read the four restatements off the slip

   A 6/12 roof is one fact written four ways. Slope: 6 / 12 = 0.5. Angle: atan(0.5) = 26.6 degrees. Percent: 0.5 x 100 = 50 percent. Multiplier: sqrt(1 + 0.5 x 0.5) = sqrt(1.25) = 1.1180. Each form has a job: the ratio is what you order materials against and tell the building department, the angle is what you set a saw or speed square to, the percent matches how graders and some codes talk, and the multiplier is the number that converts every horizontal measurement to a true along-the-slope measurement.

3. 3. Work the rafter: 24 ft span at 6/12, 2x ridge, 12 in overhang

   The run is half the span: 288 / 2 = 144 in. The ridge board takes half its thickness off each rafter, so the effective run is 144 - 0.75 = 143.25 in. The line length is the effective run times the multiplier: 143.25 x 1.1180 = 160.16 in, which is 13 ft 4 3/16 in from the ridge plumb cut to the birdsmouth plumb line. The tail adds the overhang along the same slope: 12 x 1.1180 = 13.42 in. Total rafter: 160.16 + 13.42 = 173.57 in, about 14 ft 5 9/16 in, so you buy 16 ft stock and cut down. Never order the exact length: the plumb cuts and a bad end need spare board.

4. 4. Count the rafters and check the area

   For a 20 ft long roof at 16 in on center: floor(240 / 16) + 1 = 16 rafters per side, 32 total, because both sides of the ridge need a rafter and each row starts and ends with one. At 24 in centers the same roof takes 22. For surface area, multiply the horizontal footprint by the multiplier, never use the footprint alone: a 1,400 sq ft footprint under a 6/12 roof is 1,400 x 1.1180 = 1,565 sq ft of actual roof, 15.7 squares, and roughly 52 bundles of three-per-square architectural shingles once 10 percent waste is added.

Worked scenarios, start to finish

Real jobs with the numbers carried all the way through, so you can see how the estimate is built and check your own figures against them.

The judgement calls a pro makes

Decisions the tool cannot make for you, and how someone who does this for a living thinks them through.

Where to measure a pitch you do not trust

Measure against structure, not weathered surfaces. The underside of a rafter in the attic or the rake board at the gable end gives a true line; a wavy, curled shingle field can read a half pitch off. If the attic is inaccessible, measure the rake from a ladder at the gable rather than standing on the field. And measure rise against a true 12 in of horizontal run with a level, never along the slope itself: 12 in along the slope is the classic way to read a roof shallower than it is.

Choosing an overhang: soffit depth versus looks

The overhang is a design choice the tool prices but cannot make. Twelve to 24 in is typical: deeper overhangs shade walls, throw water clear of the foundation, and need a wider soffit; short ones read modern and starve the walls of protection. The overhang is measured as horizontal projection, and the tail length grows by the multiplier, so on a steep roof a generous overhang eats surprising board length: at 12/12, an 18 in projection needs over 25 in of tail.

Picking a pitch by material and region

If you are choosing a pitch rather than measuring one, the covering and the climate decide. Asphalt wants 4/12 or better to shed cleanly with a single underlayment layer. Snow country favors 6/12 and up so the load slides rather than sits. Wind-heavy coasts often go lower and strap tighter. A steep roof costs more in rafter length, surface area, and labor (past 6/12 many crews price staging), so the multiplier row on this page is effectively a cost dial: 12/12 carries 41 percent more surface than flat.

When a 2/12 to 4/12 asphalt plan should change coverings

The IRC allows asphalt down to 2:12 with two underlayment layers, but allowed is not the same as smart. Between 2:12 and 4:12, water moves slowly, wind can push it uphill under tabs, and the double-underlayment allowance is the code admitting it. On a porch, dormer, or addition tying into that band, a membrane or a sealed-lap or standing-seam metal panel usually outlives shingles by decades. Treat the attention flag in the minimums panel as a prompt to price the alternative, not just to buy more felt.

Rafter length is geometry; rafter size is engineering

This tool tells you a 16 ft board reaches. It does not tell you whether that board should be a 2x6, 2x8 or 2x10, or whether 24 in centers carry your snow load: that comes from span tables keyed to species, grade, spacing and load, and from your local code. Get the depth and spacing from the IRC rafter span tables or an engineer, then come back here for lengths and counts. When a rafter runs past 20 ft of stock, the answer is not a longer aisle: it is a purlin, a splice designed by someone qualified, or engineered lumber.

Common mistakes, and the fix

• × Confusing slope (rise over run) with classical pitch (rise over span).

  ✓ Modern trades say pitch but mean slope: rise per 12 in of run, like 6/12. The old-book pitch divides by the whole span, so the same roof is a 1/4 pitch. If a document says a quarter pitch, that is 6/12, not 3/12. The slip shows both, labeled, so the two systems cannot get crossed.

• × Ordering shingles from the footprint area without the multiplier.

  ✓ The footprint is the horizontal shadow of the roof; the shingles lie on the slope. Multiply the footprint by the pitch multiplier first: at 8/12 the real surface is 20 percent bigger than the footprint, a four-square shortage on a modest house.

• × Forgetting the overhang adds surface and rafter length.

  ✓ Eaves hang past the walls on every side, so neither the footprint area nor the wall-to-wall rafter math includes them. Add the overhang to the area footprint (length and width grow by twice the projection) and let the tail row carry its rafter length: a 12 in overhang at 6/12 is another 13 7/16 in of board per rafter.

• × Assuming the run equals the span.

  ✓ On a gable, each rafter only crosses half the building: the run is span divided by 2. Feeding a 24 ft span in as the run doubles every length on the page. Use rise and span mode when you measured the full width and let the tool halve it.

• × Reading percent grade as degrees.

  ✓ A 50 percent slope is not 50 degrees, it is 26.6 degrees (a 6/12 roof). Percent is rise over run times 100; degrees come from the arctangent. The two scales only meet at zero, and a 100 percent slope is 45 degrees.

• × Measuring the rise over a distance other than 12 in and calling it the pitch.

  ✓ Rise per 12 in of run is the definition. If you measured 8 in of rise over 20 in of level run, normalize it: 8 / 20 x 12 = 4.8/12, call it a 5/12 roof. The rise and run mode does this arithmetic for any pair of numbers in inches or feet.

Material and unit specifics

IRC R905 minimum slopes

The 2021 IRC sets a floor per covering: asphalt shingles 2:12 (with TWO underlayment layers from 2:12 to under 4:12 per R905.1.1; one layer at 4:12 and steeper), clay and concrete tile 2 1/2:12, wood shingles and shakes 3:12, mineral-surfaced roll roofing 1:12, metal panels 3:12 with lapped nonsoldered seams, 1/2:12 when the laps are sealed, 1/4:12 for standing seam, and built-up roofing 1/4:12. These are prescriptive national figures; local amendments govern, so confirm with your building department before ordering.

Rafter stock lengths

Dimensional lumber for rafters is stocked in even lengths from 8 to 20 ft. The tool rounds the total rafter (line plus tail) up to the next stock length, because the ridge plumb cut, the birdsmouth, and squaring a shipped end all consume board. Past 20 ft, single-stick framing ends: that roof needs a purlin brace, an engineered splice, or LVL stock, all designed by someone qualified.

Ridge board versus ridge beam versus trusses

A ridge BOARD is the non-structural spacer most stick-framed gables use: rafters bear on it in opposed pairs, and each rafter gives up half its thickness, the 3/4 in deduction the tool applies for a 2x ridge. A structural ridge BEAM carries load and its deduction is half the beam width. Trusses have no field deduction at all: set the ridge option to none, and note the whole rafter conversation changes, since truss members are engineered and must never be cut.

Rafter depth and spacing are not in this tool

Nothing here sizes the rafter cross-section or the spacing for load. Whether the roof needs 2x8s at 16 in centers or 2x10s at 24 in comes from the IRC rafter span tables (or an engineer) using species, grade, snow load and span. This page computes lengths and counts for a depth and spacing you have already established. That division is deliberate: geometry is checkable arithmetic, structure is jurisdiction and load.

The measuring kit

Three cheap tools cover every method on this page: a torpedo or 24 in level and a tape for the attic 12 in method, a speed square (its common-scale markings read pitch directly when the square pivots against a rafter or rake), and a pitch gauge or a phone inclinometer app laid on the rake board for the angle. A speed square is also how the numbers leave the page: set the pitch on the common scale and mark plumb cuts and birdsmouths straight from it.

Reading your result

The x/12 figure is the roof's name: it is what you tell a supplier, a roofer, or the building department. The multiplier is the money number: every horizontal foot and every square foot of footprint grows by it, so at 1.1180 a bid based on the footprint alone is 12 percent short before waste. The angle matters at the saw and the percent matters to nobody on the roof, but both are here because plans, apps and codes speak all four dialects. Read the category chip as a labor forecast: conventional roofs get shingled off the deck, anything past 6/12 starts to carry roof jacks, staging and a steep-slope premium in quotes, and anything past 9/12 is a job to hire out unless you rig fall protection properly. The rafter rows are a lumber order: line length is what you mark between plumb cuts, the stock row is what you buy, and the count row times the stock row is the pile on the driveway. The minimums panel is a go or no-go gate per covering: green means the IRC prescriptive floor allows it at this pitch, the attention flag means allowed with conditions (the asphalt double-underlayment band), and below means pick a different covering or a different pitch. Confirm all of it locally: the numbers are national guidance, and your inspector has the last word.

Limitations

• Geometry only, no structural sizing: the tool computes rafter length and count, never rafter depth, spacing for load, ridge beam sizing, or connections. Those come from span tables, an engineer, and your local code.
• Single-plane gable math. Hips, valleys and dormers change rafter math entirely (hip and valley rafters run at a compound angle and use their own multiplier), though the pitch multiplier still applies to each roof plane for area.
• The quick area check assumes the footprint you enter already reflects the roof's horizontal extent including overhangs, and its bundle figure is a flat-plane estimate: hips, valleys, ridge caps, starters and underlayment belong in a full roofing takeoff.
• Code figures are 2021 IRC prescriptive guidance. Local amendments, manufacturer instructions (which the IRC defers to), and wind or snow provisions can be stricter, so confirm with your building department before ordering or building.
• The rafter model assumes a level plate-to-ridge common rafter with a plumb ridge cut and a birdsmouth at the plate; it does not model cathedral scissors, raised heels, or uneven-pitch gables.
• Cost uses only the price you enter times the rafter count: ridge stock, blocking, hangers, fasteners and delivery are not included.

Frequently asked questions

What is a 4/12 pitch in degrees?

A 4/12 pitch is 18.4 degrees, from atan(4/12). For quick reference: 2/12 is 9.5 degrees, 4/12 is 18.4, 6/12 is 26.6, 8/12 is 33.7, 9/12 is 36.9, 10/12 is 39.8, and 12/12 is exactly 45 degrees. The printable chart on this page runs the whole table from 1/12 to 18/12 with degrees, percent slope, and the multiplier for each.

What roof pitch is 30 degrees?

A 30 degree roof is a 6.93/12 pitch (tan 30 x 12 = 6.93), so on site it is called a 7/12. The reverse trip matters when plans give degrees but suppliers and codes speak in x/12: enter the angle in the angle mode and read the ratio off the slip, along with the 1.1547 multiplier that a 30 degree slope carries.

What is the minimum roof pitch for asphalt shingles?

Under the 2021 IRC (R905), asphalt shingles are allowed down to 2:12, but from 2:12 to just under 4:12 the code requires two layers of underlayment instead of one (R905.1.1). At 4:12 and steeper, standard single-layer underlayment applies. Below 2:12, shingles are out: use roll roofing (1:12 minimum), a sealed-lap metal panel (1/2:12), standing seam (1/4:12), or a membrane. These are national prescriptive figures, and both local amendments and the shingle manufacturer's instructions can be stricter, so confirm before ordering.

How do I measure my roof pitch from inside the attic?

Hold a level horizontal with one end touching the underside of a rafter, mark a point exactly 12 in along the level, and measure vertically from that mark up to the rafter. That vertical measurement in inches IS the pitch: 6 in means a 6/12 roof. No ladder, no walking the roof, and the rafter underside gives a truer line than a weathered shingle field. If your level is not 12 in, measure any level distance and the rise at its end, and enter the pair in rise and run mode: the tool normalizes it to x/12 for you.