Roof Pitch Calculator

How to use the roof pitch calculator

Roof pitch is the number most roofing and framing jobs start from. It decides which roof coverings the building code allows, how long the rafters are, how much roof surface there is to cover, and how dangerous the roof is to work on. This roof pitch calculator works it out from whatever you can measure, shows every formula it uses on this page, and keeps all of the math in your browser.

1. Pick what you know. On the Pitch tab, choose rise and run, a pitch (x/12), an angle in degrees, a slope percentage, rise and rafter length, or run and rafter length. Length fields take feet and inches with fractions, such as 14' 3 5/8", plain inches, or millimeters.
2. Read the results. You get the pitch as x/12 and in words ("6 in 12"), the angle in decimal degrees and in degrees, minutes and seconds, the slope percentage, the reduced ratio, the pitch factor and hip/valley factor, the rafter length per foot of run, the plumb and seat cut angles and the framing-square settings. A diagram draws the triangle to your pitch, and a short list shows which roof coverings the code allows at that pitch.
3. Work out the rafters. The Rafters tab takes the building width, pitch, overhang, ridge board and rafter depth, and returns the common rafter length, the ridge deduction, the board length and the stock length to buy, the hip and valley length and a rafter count.
4. Can't reach a rafter? Don't climb up. From a photo measures the pitch on a picture you take from the ground, and Phone level turns a phone into a pitch gauge you can rest on a rafter in the attic. Pitch chart lists every whole pitch from 0/12 to 24/12.

The same tool works as a roof slope calculator, a roof angle calculator, a rafter length calculator and a roof pitch finder. Switch Units to Metric for millimeters and degrees; switch Precision to show lengths to the nearest 1/8", 1/16" or 1/32", or as decimals.

What roof pitch means

Roof pitch is how steeply a roof rises, written as the inches of vertical rise for every 12 inches of horizontal run. A roof that climbs 6 inches over 12 inches of run is a 6/12 pitch, said "6 in 12" and sometimes written 6:12. Run is measured level, never along the roof surface, and the 12 is simply one foot: a 6/12 roof gains 6 inches of height for every foot you move in from the wall toward the ridge.

Three other numbers describe the same steepness, and the calculator shows all of them:

• Angle: the angle between the roof surface and level, in degrees. A 6/12 roof is at 26.57°.
• Slope percentage: rise ÷ run × 100. A 6/12 roof is a 50.00% slope, because 6 is half of 12.
• Ratio: rise to run in lowest terms. A 6/12 roof is 1:2, or "1 in 2", and a 4/12 roof is 1:3.

In everyday U.S. use, "pitch" and "slope" mean the same thing, the rise per 12 inches of run, and this page uses them that way. The building code writes the same idea as "units vertical in 12 units horizontal", with a percentage in parentheses. Some older carpentry texts, including the U.S. Army's 1995 carpentry manual (FM 5-426), define pitch as the rise divided by the span, the full width of the building, so a "1/4 pitch" roof under that definition is what we now call 6/12.

The calculator also sorts pitches into four groups: flat (below 2/12), low (2/12 to under 4/12), conventional (4/12 to under 8/12) and steep (8/12 and up). That is our own rough grouping, not a code or OSHA definition; the codes and OSHA draw their lines elsewhere, as the section on minimum pitch explains.

Roof pitch formulas

Pitch, angle and slope are three ways of writing the same right triangle, so each converts exactly into the others. With the rise and run in the same unit:

pitch (x/12)     = rise ÷ run × 12
slope %          = rise ÷ run × 100
angle            = arctan(rise ÷ run)
pitch from angle = 12 × tan(angle)
pitch factor     = √(1 + (pitch ÷ 12)²)

In a spreadsheet with the pitch (the x in x/12) in cell A2, the angle in degrees is =DEGREES(ATAN(A2/12)) and the pitch for an angle in B2 is =12*TAN(RADIANS(B2)).

Example 1: a 6/12 pitch in degrees (pitch to degrees)

A 6/12 roof rises 6 inches over 12. The slope is 6 ÷ 12 = 0.5, or 50.00%, and the angle is arctan(0.5) = 26.57°, which is 26° 33′ 54″. The pitch factor is √(1 + 0.5²) = 1.118, so every foot of run takes 13 7/16" of rafter. As a ratio, 6/12 is 1:2.

Example 2: 30 degrees to pitch (degrees to pitch)

To convert degrees to pitch, multiply the tangent of the angle by 12. For 30°, that is 12 × 0.57735 = 6.93, a 6.93/12 pitch. The nearest whole or half pitch is 7/12; the calculator shows both, and suggests the nearest half-inch pitch whenever yours isn't a whole or half number.

Example 3: a 4/12 pitch in degrees and percent

A 4/12 pitch is a slope of 4 ÷ 12 = 33.33% and an angle of arctan(1/3) = 18.43°. Its pitch factor is 1.054, and its hip/valley factor is 1.453.

Slope percentage to pitch

Multiply the percentage by 12 and divide by 100. A 25% slope is 25 × 12 ÷ 100 = 3 inches of rise per foot, a 3/12 pitch at 14.04°.

Roof pitch chart

The roof pitch chart below converts every whole pitch from 1/12 to 24/12 into degrees, slope percentage, pitch factor (the roof pitch multiplier), hip/valley factor and rafter length per foot of run. It is computed by the same code as the Pitch chart tab, which also has 0/12, highlights your current pitch, loads any row into the calculator and downloads the chart as a CSV file.

To read it, find your pitch in the first column. The angle is the roof's slope in degrees, the slope is rise ÷ run as a percentage, and the pitch factor is how much longer the roof surface is than its level run. A 12/12 roof is exactly 45°, a 100.00% slope, with a factor of 1.414; every row below it is steeper than 45 degrees. The last column is the pitch factor times 12 inches, rounded to the nearest 1/16".

Common angles to pitch

Going the other way, from degrees to pitch, rarely lands on a whole number. This table shows the exact pitch for some round angles and the nearest whole or half pitch:

How to measure roof pitch

The classic method uses a level and a tape measure on a rafter in the attic, where you are standing on the ceiling framing rather than on the roof. Step on the joists or a board laid across them, never on the ceiling between them.

1. Stay off the roof. Work from the attic or from the ground with a photo. From a ladder, use only the one-handed phone method, keeping three points of contact. The photo and phone methods are described below.
2. Hold a level against a rafter. In the attic, hold a level horizontally, with the bubble centered and one end touching the underside of a rafter.
3. Mark 12 inches along the level. Measure 12 inches along the level from the end that touches the rafter, and mark the spot.
4. Measure straight up to the rafter. From the mark, measure plumb (vertically) up to the underside of the rafter. That distance is the rise per 12 inches of run: 6 inches means a 6/12 pitch. The rafter's edges are parallel, so its depth doesn't change the answer.
5. Enter it in the calculator. On the Pitch tab, choose Rise & run and enter the rise with a run of 12 inches. For more accuracy, measure over a longer run, such as 24 inches, and enter both numbers: a 12-inch rise over 24 inches is still 6/12.

At the gable end

If you can't get into the attic, the rake board (the trim along the sloped edge of a gable) has the same pitch as the roof. The level-and-tape method needs both hands, so use it there only on a gable end you can reach without a ladder. From a ladder, use the phone method below instead: rest the phone against the rake board with one hand, keeping both feet and your other hand on the ladder. Follow OSHA's ladder advice: place the ladder on stable and level ground, do not work on the top rung, and maintain three points of contact with the ladder at all times. For a leaning ladder, OSHA's ladder rule sets the foot out about a quarter of the ladder's working length from the top support, often called the 4-to-1 rule.

From the ground: measure from a photo

To measure roof pitch from the ground, take a photo of a gable end and open it in From a photo. Drag the two handles onto the ends of the sloped rake edge, and the tool reads the angle and the pitch. A few things make the estimate better:

• Stand square to the gable end. A photo taken from an angle makes the roof look steeper than it is.
• Stand as far back as you can and zoom in, rather than shooting wide up close: perspective distortion shrinks with distance. Keep the camera level and the roof line near the middle of the frame, where lens distortion is lowest.
• Mark the main rake edge, not a dormer, a porch or a hip, which may have a different pitch.
• If the photo is tilted, switch on the level line and mark something truly horizontal in the same wall, such as the fascia along the eave, a siding course or a window head. That corrects a rotated photo, not perspective.

The photo never leaves your device. Treat the result as an estimate, and confirm it with a level before you order material or cut anything.

With your phone

The Phone level tab turns a phone into a roof pitch finder, with no app to install. Tap Start (some phones ask for permission to use motion sensors), then place the phone. In the default Long edge along the slope mode, lay the phone flat on the underside of a rafter with its long edge running along the rafter, or stand it on its long edge against the side of a rafter or the rake board; sideways roll doesn't affect this reading. In Lying flat on the surface mode, the phone must lie flat on the sloped surface itself, such as the underside of the roof sheathing between two rafters. Zero it on a known-level surface first, wait for the reading to settle and tap Hold.

Phone sensors are close but not exact. In one small validation study, one phone consistently read about 1.1° low against precision angle blocks, and the authors recommended a zeroing feature, which the tool has. Take the phone out of a bulky case, and check the result with a level before cutting.

From plans or known dimensions

Building plans often mark the pitch on the roof elevations or sections with a small triangle: 12 on the level leg and the rise on the vertical one. If you know the building width and how far the ridge rises above the top of the walls, enter them as rise and run (half the width) or use the span and rise example below.

Pitch from rise and run, or from a rafter length

When you know two lengths rather than an angle, the calculator solves the right triangle for you. Rise and run have to be in the same unit, but it doesn't matter which: feet, inches or millimeters all give the same pitch.

Example 4: a 3 ft rise over a 9 ft run

A roof that rises 3' 0" over a run of 9' 0" has a pitch of 3 ÷ 9 × 12 = 4/12, an angle of 18.43°. The sloped length over that run is √(3² + 9²) feet, or 9' 5 13/16".

Example 5: a 12 ft run and a 13 ft rafter

If you know the run and the sloped length, the rise is √(13² − 12²) = 5' 0", so the pitch is 5/12, at 22.62°. Starting from the rise and the sloped length instead, 5' 0" and 13' 0", gives the same 5/12. The sloped length here is measured between the same two points as the run and the rise; it is not the length of the board you buy, which the next sections cover. The rafter can't be shorter than the run, and it has to be longer than the rise.

Example 6: building width and ridge height

On a gable roof the run is half the building width, called the span. A building 24' 0" wide whose roof rises 4' 0" from the top of the walls to the ridge at the centerline has a run of 12' 0" and a pitch of 4/12. Measure the span and the rise to the same lines, for example the outside of the wall framing and the top of the wall plate.

Roof pitch multiplier and roof area

The pitch factor, also called the roof pitch multiplier or slope factor, is the length of sloped roof per unit of level run: √(1 + (pitch ÷ 12)²). Because every plane of a roof is tilted by the same amount in one direction, the same factor converts a roof plane's plan area, the area you'd see from directly above, into its true surface area:

roof area = footprint area × pitch factor
squares   = roof area ÷ 100

Example 7: a 1,500 sq ft footprint at 6/12

Start from the footprint's square footage: the area inside the outline of the roof seen from above, overhangs included.

A roof whose footprint, overhangs included, measures 1,500 sq ft at a 6/12 pitch has a surface area of 1,500 × 1.118 = 1,677.05 sq ft, or 16.77 squares. In roofing, a square is 100 sq ft of roof surface.

This only holds when every plane of the roof has the same pitch; for a roof with several pitches, work out each part separately and add them. The footprint field under Roof area from the footprint on the Pitch tab does this multiplication. To turn the area into shingle bundles, underlayment, waste and a cost estimate, use the Roofing Calculator.

Rafter length

A common rafter runs from the wall plate to the ridge at right angles to both. Its length comes from the run and the pitch factor, with three corrections: half of the ridge board comes off the top, the overhang goes on the bottom, and the plumb cut at the top needs a little extra board.

run           = span ÷ 2 (gable) or span (shed)
line length   = (run − ridge thickness ÷ 2) × pitch factor
overhang      = eave overhang × pitch factor
total length  = line length + overhang
board length  = total length + rafter depth × pitch ÷ 12
hip or valley = run × √(2 + (pitch ÷ 12)²)

Example 8: a 24 ft wide gable at 6/12

Lengths are along the rafter and assume a straight, uncrowned board; add a few inches for trimming. The count is a layout count: gable-end rafters, doubled rafters at openings and the ridge itself vary from roof to roof. Rafter size and span depend on lumber species, grade, spacing and loads, so this page gives neither: check the IRC span tables (Section R802.4.1, Tables R802.4.1(1) through R802.4.1(8)) or ask an engineer. The IRC measures a rafter span "along the horizontal projection of the rafter", which is not the same as the building width used here.

Cut angles and the framing square

Two cuts set a rafter's pitch. The plumb cut at the ridge (and often at the tail) is vertical once the rafter is in place; the seat cut of the birdsmouth sits level on the wall plate. Measured against the rafter's edge, they are 90 degrees minus the roof angle and the roof angle itself.

For a 6/12 roof, the plumb cut meets the rafter's edge at 63.43° and the seat cut at 26.57°. The plumb cut is the roof angle off square, so on a miter saw with the rafter lying flat the miter setting is 26.57°; with the board standing on edge against the fence, the same figure goes on the bevel scale. A circular saw following a marked plumb line stays square. At steep pitches the angle can be more than a miter saw's scale reaches, so mark the line and cut it by hand or with a circular saw.

With a framing square, hold 12 on the body (the wide arm) and the rise on the tongue against the rafter's edge: 12 and 6 for a 6/12 roof. Mark along the tongue for the plumb cut and along the body for the seat cut. Hip and valley rafters use 17 on the body instead of 12, because a hip covers about 17 inches of diagonal run (12 × √2) for every 12 inches of common run, so a 6/12 hip is laid out at 17 and 6. The calculator lists both settings for your pitch. The same rise-over-run layout is used for stair stringers, though stairs have their own code limits.

Minimum roof pitch by roofing material

Every roof covering has a lowest pitch it may be installed on, because water drains slowly off a shallow roof and wind can drive it back up under the laps. The International Residential Code (IRC), the model code for houses published by the International Code Council, sets those minimums in Section R905. The table gives the minimum pitch for each covering in the 2024 edition; the 2021 edition has the same minimums, though some section numbers differ. The Pitch tab checks your pitch against the same list.

Minimum pitch for shingles. Section R905.2.2 says asphalt shingles "shall be used only on roof slopes of 2 units vertical in 12 units horizontal (17-percent slope) or greater", and that from 2 in 12 up to 4 in 12 "double underlayment application is required in accordance with Section R905.1.1." The 2024 underlayment table allows a single layer of self-adhering polymer-modified bitumen underlayment that complies with ASTM D1970 instead of the two layers. In areas where the code requires wind design, the extra underlayment applies at every pitch. Wood shingles and wood shakes both start at 3/12, and slate at 4/12.

Minimum slope for a metal roof depends on the kind of metal roof. Metal shingles and lapped, nonsoldered-seam panels without lap sealant need 3/12; lapped panels with an applied lap sealant can go down to ½ in 12, and standing-seam systems to ¼ in 12 (Section R905.10.2). The coverings listed at ¼/12 are given as a design slope "for drainage": the slope the roof is built to so that water runs off. These are minimum slopes only; maximum slopes and other limits come from the manufacturer.

These figures are code minimums only: local codes and the manufacturer's installation instructions govern, and many manufacturers ask for more than the code does. Check with your building department before you choose a covering for a low-pitched roof.

Low slope and steep slope

These words mean different things in different documents. The building codes split at 2 in 12: the International Building Code (Section 202) and the 2024 IRC's energy chapter (Section N1101.6) call a roof slope of 2 units vertical in 12 units horizontal or greater a steep slope, and anything less a low slope. OSHA's construction fall-protection rules call a roof low-slope at 4 in 12 or less and steep above 4 in 12 (29 CFR 1926.500(b)). So a 4/12 roof is "conventional" in the calculator's rough grouping, a steep slope to the building codes and a low-slope roof to OSHA. Under 29 CFR 1926.501, employers must protect workers on either kind of roof from falls once they are six feet or more above a lower level.

Common roof pitches

A handful of pitches come up again and again in questions, plans and charts. Here is what each one means in numbers and under the code; none is better than another, and the right pitch for a building depends on its design, climate and covering.

• 3/12 pitch: 14.04°, a 25.00% slope. Asphalt shingles are allowed but need the extra underlayment, and it is the code minimum for metal roof shingles, wood shingles, wood shakes and lapped metal panels without sealant.
• 4/12 pitch: 18.43°, 33.33%, pitch factor 1.054. From here up, asphalt shingles need only one layer of underlayment (where wind design isn't required), and it is the minimum for slate. It is also the top of OSHA's low-slope range.
• 5/12 pitch: 22.62°, 41.67%. Each foot of run takes exactly 13" of rafter, because 5, 12 and 13 form a right triangle.
• 6/12 pitch: 26.57°, 50.00%, a 1:2 ratio and a pitch factor of 1.118. The calculator's default, and the example used throughout this page.
• 8/12 pitch: 33.69°, 66.67%, pitch factor 1.202. Where the calculator's "steep" group starts. Where the IRC requires an ice barrier, roofs of 8 units vertical in 12 units horizontal or more need it to reach at least 36 inches along the slope from the eave edge (R905.1.2).
• 9/12 pitch: 36.87°, 75.00%. Exactly 15" of rafter per foot of run, from the 3-4-5 triangle.
• 12/12 pitch: 45°, a 100.00% slope where the rise equals the run. The pitch factor is 1.414, so every square foot of footprint carries that many square feet of roof.

Metric: pitch in degrees and millimeters per meter

In metric units, roof pitch is often given in degrees, as a percent, or in millimeters of rise per meter of run. Switch Units to Metric and the calculator leads with the angle, takes lengths in millimeters (or with cm or m after the number), shows lengths in whole millimeters, and gives rafter length per meter of run instead of per foot.

The math is identical: one inch is exactly 25.4 mm. A 30° roof rises 577 mm for each meter of run, and each meter of run takes 1,155 mm of rafter; in x/12 terms it is 6.93/12. A 22.5° roof rises 414 mm per meter, with 1,082 mm of rafter per meter of run. In metric mode, the stock lengths offered for rafters run from 1.8 m to 6.0 m in 0.3 m steps, a typical range; what you can buy varies by region and supplier.

How we calculate

Every figure on this page and in the tool comes from the same code, and the examples above are checked against it automatically. These are the rules it follows:

• Pitch is stored as the rise per 12 units of run. Angle = arctan(pitch ÷ 12); slope = pitch ÷ 12; pitch factor = √(1 + slope²); hip/valley factor = √(2 + slope²), for equal pitches meeting at a right angle; hip line angle = arctan(slope ÷ √2).
• Two lengths. Run = √(rafter² − rise²) or rise = √(rafter² − run²); on a gable, run = span ÷ 2. The rafter has to be longer than the rise and at least as long as the run.
• Rafters. Line length = (run − ridge ÷ 2) × factor; overhang length = overhang × factor; board length = total length + depth × slope; heel cut = seat cut × slope. Stock lengths are 8 to 24 ft in 2 ft steps, or 1.8 to 6.0 m in 0.3 m steps; anything longer is flagged so you can splice or order engineered lumber. Rafter count = length ÷ spacing, rounded up, plus one, per side.
• Photo. The angle of the line you mark, measured from the picture's horizontal or from a level line you mark, folded into 0 to 90 degrees.
• Phone. From the device's orientation sensor (β and γ are its front-to-back and side-to-side tilt). In Long edge along the slope mode, the angle of the phone's long edge, arcsin(|sin β|), which ignores sideways roll; in Lying flat on the surface mode, the tilt of the screen, arccos(cos β × cos γ). Averaged over the last ten readings, minus the zero offset if you set one.
• Full precision, rounded for display. Results are kept unrounded. Lengths are shown to the nearest 1/16" by default, with the carry into feet (11.99" shows as 1' 0"), or to whole millimeters in metric. Angles and percentages show two decimals, factors three, and pitches up to two decimals; the nearest whole or half pitch is the nearest half inch of rise.
• Limits. Angles up to 85° and lengths up to 10,000 ft. Lengths are along the rafter and assume a straight, uncrowned board.

Your photo and sensor readings stay on your device

The calculator runs entirely as JavaScript in your browser tab, so your measurements, your photo and your phone's sensor readings never leave the device.

• Photos are never uploaded. The picture you choose is read by the page itself and shown from memory. The page's Content-Security-Policy only allows connections back to this site, and the tool has no code that sends anything anywhere.
• Sensor readings aren't stored or sent. The phone level reads the orientation sensor only after you tap Start and uses the readings to draw the angle. The only thing it saves is the zero offset, if you set one, in this browser on your device.
• No account, no cookies. The tool remembers your last inputs, units and tab in your browser's local storage, on your device only. It never stores the photo.

Sources

• International Code Council: 2024 International Residential Code, Chapter 9 Roof Assemblies, Section R905 (minimum slopes and underlayment, Table R905.1.1(2)) and R905.1.2 (ice barrier).
• International Code Council: 2021 International Residential Code, Chapter 9 Roof Assemblies, the same minimums under the previous edition's section numbers.
• International Code Council: 2024 International Residential Code, Chapter 8 Roof-Ceiling Construction, Section R802.4.1 (rafter size and span tables) and R802.3 (ridge).
• International Code Council: 2024 International Residential Code, Chapter 11 Energy Efficiency, Section N1101.6 (low slope and steep slope).
• International Code Council: 2024 International Building Code, Chapter 2 Definitions, Section 202 (low-slope and steep-slope).
• 29 CFR 1926.500, Scope, application, and definitions (eCFR), and the same text on OSHA's site: low-slope and steep roof definitions.
• OSHA: 29 CFR 1926.501, Duty to have fall protection.
• OSHA: Fall Prevention Campaign and OSHA: Fall Protection.
• OSHA: Falling Off Ladders Can Kill: Use Them Safely (OSHA 3625) and 29 CFR 1926.1053, Ladders.
• U.S. Department of the Army: FM 5-426, Carpentry (1995), Chapter 7 and Glossary, for the older rise-over-span definition of pitch.
• Guardia A, Khan MI, Donauer A, Duke K. Validation of smartphone inclinometer tools for measuring rib hump in scoliosis patients. Scoliosis 2015;10(Suppl 1):O28 (PubMed Central), on phone inclinometer accuracy and zeroing.

Reviewed by microplugins · Last updated October 2026

This is an educational tool, not engineering, building-code or construction advice. Code requirements vary by location and edition: check with your building department, follow the roofing manufacturer's installation instructions, and have a qualified professional size and check any framing.