Roof Pitch Calculator — Angle, Rise & Rafter Math

How to Measure Roof Pitch

Roof pitch is the steepness of a roof, expressed as a ratio of vertical rise to horizontal run. Standard convention uses a 12-inch run, so a roof that rises 4 inches over 12 inches of horizontal distance has a 4/12 pitch.

The simplest way to measure roof pitch from inside an attic:

Step 1: Use a level and a tape measure. Hold a 12-inch level horizontally against the underside of a rafter, with one end of the level touching the rafter. Make sure the level reads true.

Step 2: From the free end of the level, measure straight up to the underside of the rafter. The distance you measure is your pitch numerator.

Step 3: Express it as a fraction over 12. If you measured 4 inches, the pitch is 4/12. If you measured 6 inches, it's 6/12. If you measured 8 inches, it's 8/12.

For roofs you can't access from inside, you can measure from outside using a similar method on the gable end, or use a smartphone level app placed on the roof surface. The app gives you the angle in degrees, which converts to pitch using the chart in the next section.

Pitch calculation summary:

• Rise (inches) over run (12 inches) = pitch
• Example: 4 inches rise over 12 inches run = 4/12 pitch
• Example: 8 inches rise over 12 inches run = 8/12 pitch (steep)

The calculator above does this conversion automatically. Just enter your rise and run measurements.

Common Roof Pitches and What They're Used For

Roof pitch isn't arbitrary — different pitches serve different climates, architectural styles, and structural purposes.

Common residential roof pitches:

• 2/12 pitch — Low-slope roof (almost flat). Used for porches, additions, and modern architecture. Requires special roofing materials (membrane, rolled roofing) since shingles aren't watertight on slopes this low.
• 3/12 pitch — Minimum pitch for asphalt shingles (with special underlayment). Common for ranch-style homes and additions in mild climates.
• 4/12 pitch — Standard pitch for many ranch and bungalow homes. Walkable for most contractors. Sheds water effectively.
• 5/12 pitch — Common for traditional residential. Excellent water shedding.
• 6/12 pitch — Standard for Cape Cod and colonial homes. The maximum walkable pitch for most workers without fall protection.
• 7/12 to 8/12 pitch — Steep residential. Common for traditional architecture, snow-load regions. Requires fall protection equipment.
• 9/12 to 12/12 pitch — Very steep. Victorian, gothic, and chalet-style homes. Excellent for snow-shedding climates.
• 12/12 pitch — 45-degree angle. Common ceiling for steepness in most residential builds.
• Above 12/12 — Steep architectural roofs. Specialty work only.

Most home roofs are between 4/12 and 8/12. Roofs below 3/12 require special consideration for waterproofing. Roofs above 12/12 require specialty contractors and increase labor costs significantly.

Roof Pitch to Degrees Conversion

Converting between pitch (rise/run format) and degrees uses basic trigonometry: degrees = arctan(rise ÷ run).

Common pitch-to-degree conversions:

• 1/12 pitch — 4.76 degrees
• 2/12 pitch — 9.46 degrees
• 3/12 pitch — 14.04 degrees
• 4/12 pitch — 18.43 degrees
• 5/12 pitch — 22.62 degrees
• 6/12 pitch — 26.57 degrees
• 7/12 pitch — 30.26 degrees (close to "30 degree roof pitch")
• 8/12 pitch — 33.69 degrees
• 9/12 pitch — 36.87 degrees
• 10/12 pitch — 39.81 degrees
• 11/12 pitch — 42.51 degrees
• 12/12 pitch — 45 degrees
• 15/12 pitch — 51.34 degrees
• 18/12 pitch — 56.31 degrees

Common questions answered:

• A 30-degree roof has approximately a 7/12 pitch
• A 45-degree roof has exactly a 12/12 pitch
• A 60-degree roof has a 21/12 pitch (rare in residential)

The calculator above handles both directions — input pitch to get degrees, or input degrees to get pitch.

Roof Pitch Multiplier — Calculating Roof Surface Area

The roof pitch multiplier is a number that, when multiplied by your home's footprint, gives you the actual roof surface area. It accounts for the additional surface created by the slope.

The multiplier increases with steeper pitches because steeper roofs have more surface area per square foot of ground covered.

Standard pitch multipliers:

• 2/12 pitch — 1.014 multiplier
• 3/12 pitch — 1.031 multiplier
• 4/12 pitch — 1.054 multiplier
• 5/12 pitch — 1.083 multiplier
• 6/12 pitch — 1.118 multiplier
• 7/12 pitch — 1.158 multiplier
• 8/12 pitch — 1.202 multiplier
• 9/12 pitch — 1.250 multiplier
• 10/12 pitch — 1.302 multiplier
• 11/12 pitch — 1.357 multiplier
• 12/12 pitch — 1.414 multiplier
• 15/12 pitch — 1.601 multiplier
• 18/12 pitch — 1.803 multiplier

How to use the multiplier:

If your home has a 1,500 sq ft footprint and a 6/12 roof pitch, the actual roof surface area is approximately 1,500 × 1.118 = 1,677 sq ft.

For roofing material estimates (shingles, underlayment, ice and water shield), use the multiplied surface area, not the footprint. Roofing contractors charge by "squares" — 1 square = 100 sq ft of roof surface. The example above is 16.77 squares.

Add 10% for waste in cuts and overlaps when ordering materials. So 16.77 squares becomes 18.5 squares ordered.

Rafter Length Calculator

Rafter length depends on three things: roof pitch, building width, and overhang. Once you know your pitch and run, the rafter length follows directly from the Pythagorean theorem.

The rafter length formula:

Rafter length = √(rise² + run²)

Where rise and run are the rafter's actual rise and run, not the pitch ratio.

For a typical residential build:

A 30-foot wide home with a 6/12 pitch and 12-inch overhang:

• Run = (30 ÷ 2) + 1 = 16 ft (half the building width plus overhang)
• Rise at 6/12 pitch = 16 × 0.5 = 8 ft
• Rafter length = √(8² + 16²) = √(64 + 256) = √320 = 17.89 ft

So each rafter on this home is 17.89 ft from ridge to overhang end.

Common rafter lengths by pitch (24-foot wide home, 12-inch overhang):

• 3/12 pitch: 13.34 ft
• 4/12 pitch: 13.60 ft
• 5/12 pitch: 13.93 ft
• 6/12 pitch: 14.32 ft
• 7/12 pitch: 14.76 ft
• 8/12 pitch: 15.23 ft
• 12/12 pitch: 18.38 ft

Always order rafters longer than your calculation by 6 to 12 inches to allow for the birdsmouth cut at the wall plate and the plumb cut at the ridge. Trim to exact length on-site.

The calculator above gives precise rafter lengths for any pitch and run combination.

Rise and Run Calculator

Rise and run are the foundational measurements for any roof pitch calculation. Rise is the vertical height from the wall plate to the ridge. Run is half the building width (or, for hip roofs, the distance from one wall plate to the centerline).

For a standard gable roof:

• Run = (Building width) ÷ 2
• Rise = Run × (pitch numerator ÷ 12)

Worked example:

A 28-foot wide home with a 6/12 pitch:

• Run = 28 ÷ 2 = 14 ft
• Rise = 14 × (6 ÷ 12) = 14 × 0.5 = 7 ft

So the ridge sits 7 feet above the top of the wall plates.

Common rise calculations by pitch (for a 24-foot wide home):

• 3/12 pitch: 3 ft rise
• 4/12 pitch: 4 ft rise
• 5/12 pitch: 5 ft rise
• 6/12 pitch: 6 ft rise
• 7/12 pitch: 7 ft rise
• 8/12 pitch: 8 ft rise
• 12/12 pitch: 12 ft rise

This calculation assumes a simple gable roof. For complex roofs (hip, gambrel, mansard), the rise calculation differs at intersection points. The calculator above handles standard gable rise/run; for complex roofs, work directly with framing plans.

Birdsmouth Cut Calculator

The birdsmouth cut is the notch cut into the bottom of a rafter where it meets the top wall plate. It allows the rafter to sit flat on the wall while the rafter continues upward at the roof pitch.

The birdsmouth has two cuts:

1. Seat cut — horizontal cut where the rafter rests on the wall plate
2. Plumb cut — vertical cut where the rafter meets the wall plate's outside edge

Standard birdsmouth dimensions:

• Seat cut depth: should not exceed 1/3 the rafter's depth
• Seat cut length: typically 3.5 inches (for a 2x4 wall) or 5.5 inches (for a 2x6 wall)
• Plumb cut: cuts at the same angle as the roof pitch

Birdsmouth measurements by pitch (for a 2x10 rafter on a 2x6 wall):

• 4/12 pitch — Seat cut 5.5", plumb cut at 18.4° angle
• 5/12 pitch — Seat cut 5.5", plumb cut at 22.6° angle
• 6/12 pitch — Seat cut 5.5", plumb cut at 26.6° angle
• 7/12 pitch — Seat cut 5.5", plumb cut at 30.3° angle
• 8/12 pitch — Seat cut 5.5", plumb cut at 33.7° angle
• 12/12 pitch — Seat cut 5.5", plumb cut at 45° angle

Marking the birdsmouth:

Use a framing square. The body of the square represents the seat cut; the tongue represents the plumb cut. Set the square to your pitch (e.g., 6 on the body, 12 on the tongue) and trace the inside edge.

The calculator above gives birdsmouth dimensions for any pitch and rafter size. For complex framing (hip rafters, valley rafters), the birdsmouth angle changes — those use the multiplied pitch rather than the simple rafter pitch.

Shed Roof Pitch Calculator

Shed roofs are single-slope roofs that pitch in only one direction (no ridge). They're common on additions, modern architecture, and actual sheds.

Shed roof pitch considerations:

• Minimum recommended pitch: 1/12 (with membrane roofing) or 3/12 (with shingles)
• Standard shed pitch: 4/12 to 6/12 — sheds water well, walks reasonably
• Maximum practical pitch: 12/12 — anything steeper looks awkward on a shed

For a shed roof, calculate pitch differently than gable:

• Rise = ridge height minus eave height
• Run = full width of the shed (not half, since there's no center peak)

Worked example:

A 12-ft wide shed with the high side at 10 ft and the low side at 7 ft:

• Rise = 10 - 7 = 3 ft (36 inches)
• Run = 12 ft (144 inches)
• Pitch = 36/144 = 3/12

Common shed pitches and uses:

• 1/12 to 2/12 — Modern flat-look sheds (requires membrane)
• 3/12 to 4/12 — Standard storage sheds with shingles
• 5/12 to 6/12 — Traditional shed look, good water shedding
• 7/12 and above — Decorative or steep-design sheds

The calculator above handles shed roofs the same as gable — just enter the rise (height difference) and run (shed width).

How to Calculate Roof Pitch in Degrees

If you have a measured pitch in rise/run format and need to convert to degrees, use the formula:

Degrees = arctan(rise ÷ run)

For a standard pitch with run = 12:

• 4/12 pitch: arctan(4/12) = arctan(0.333) = 18.43°
• 6/12 pitch: arctan(6/12) = arctan(0.5) = 26.57°
• 8/12 pitch: arctan(8/12) = arctan(0.667) = 33.69°

If you only have an angle measurement (from a smartphone level app, for example) and need to convert to pitch:

Pitch ratio = tan(degrees)

Then express as fraction over 12:

• 30°: tan(30) = 0.577 → 0.577 × 12 = 6.93 → roughly 7/12 pitch
• 45°: tan(45) = 1.0 → 1 × 12 = 12 → 12/12 pitch
• 60°: tan(60) = 1.732 → 1.732 × 12 = 20.78 → roughly 21/12 pitch

Why this matters in practice:

Construction drawings typically show pitch in rise/run. Building permits sometimes require degrees. Solar panel installers prefer degrees. Knowing how to convert in either direction lets you communicate with all parties without confusion.

The calculator above does both conversions automatically.

Roof Pitch vs. Roof Slope vs. Roof Angle

These three terms get used interchangeably in casual conversation but mean slightly different things technically.

Roof pitch — The ratio of vertical rise to horizontal run, traditionally expressed as X/12 (e.g., 6/12). Standard in carpentry and roofing.

Roof slope — Sometimes used as a synonym for pitch, but more often refers specifically to the rise as a fraction of the rafter length (rather than the run). Used more often in engineering and ADA compliance documents.

Roof angle — The pitch expressed in degrees (e.g., 26.57°). Used in math, solar installations, and architectural drawings.

The three are mathematically related:

• A 6/12 pitch
• = a 6:13.42 slope
• = a 26.57° angle

In practice, North American residential construction defaults to pitch (X/12). European and academic contexts prefer degrees. Solar installers use degrees because solar panel manufacturers spec optimal angles in degrees.

When working with contractors, use pitch. When working with engineers or solar installers, use degrees. The calculator above shows all three for clarity.

Hip Rafter Calculator

Hip rafters run diagonally from the corner of a building to the ridge. Because they travel diagonally, they're longer than common rafters and use a different calculation.

Hip rafter length formula:

Hip rafter length = √(common rafter length² + run²)

Where the run for hip rafters is the diagonal run, calculated as:

Hip run = √(building width² + building length²) ÷ 2

(For a square or symmetrical building; asymmetrical hip roofs use different geometry.)

Worked example:

A 24-ft × 36-ft home with a 6/12 pitch:

• Building diagonal = √(24² + 36²) = √(576 + 1,296) = √1,872 = 43.27 ft
• Hip run = 43.27 ÷ 2 = 21.64 ft
• Common rafter rise (using width) = 12 × 0.5 = 6 ft
• Hip rafter length = √(21.64² + 6²) = √(468.29 + 36) = √504.29 = 22.46 ft

So each hip rafter on this home is approximately 22.46 ft from the corner to the ridge, before adding overhang.

Hip rafters require:

• A different birdsmouth angle (uses 17/12 multiplier for the seat cut)
• Cheek cuts at the ridge end (because they meet other rafters at angles)
• Sized larger than common rafters (typically 2x12 vs. 2x10) due to longer span

For non-standard hip roof builds (irregular footprints, asymmetric hips), work directly from architectural framing plans rather than calculator estimates.

Step-by-Step — How to Calculate Roof Pitch

If you want to verify the calculator output or learn the math yourself, here's the complete process.

Step 1: Get inside the attic safely

Most accurate measurements come from inside, where you can directly access the underside of the rafters. Use proper safety equipment and adequate lighting.

Step 2: Find a rafter and mark a reference point

Pick a rafter that runs from wall plate to ridge. Make a small pencil mark on the underside, ideally near the middle of its length where the slope is consistent.

Step 3: Hold a 12-inch level horizontally

Place one end of a 12-inch level against the underside of the rafter at your mark. Hold the other end horizontally — the bubble should be centered.

Step 4: Measure the gap

From the free end of the level (the end NOT touching the rafter), measure straight up to the underside of the rafter. This vertical distance is your rise over a 12-inch run.

Step 5: Express as pitch

If you measured:

• 3 inches → 3/12 pitch
• 4 inches → 4/12 pitch
• 5 inches → 5/12 pitch
• 6 inches → 6/12 pitch
• 7 inches → 7/12 pitch (close to 30 degrees)
• 8 inches → 8/12 pitch
• 12 inches → 12/12 pitch (45 degrees)

Step 6: Verify on a second rafter

Measure another rafter to confirm. All rafters on the same roof plane should give the same pitch reading. Different readings suggest the level isn't truly horizontal or one of the rafters has settled.

Alternative method — exterior measurement:

If attic access isn't possible, measure pitch at the gable end. Place a 12-inch level horizontally against the rake (the sloped edge of the roof at the gable end), with one end touching. Measure vertically from the free end of the level up to the rake board.

Smartphone method:

Most smartphones have a built-in level. Open the level app, place the phone flat on the roof surface (carefully — fall safety first), and read the angle. Convert to pitch using the conversion table above.

The calculator above does the conversion automatically once you input your measurements.

Roof Pitch Quick-Reference Tables

For fast estimating without the calculator, these benchmarks cover the most common scenarios.

Pitch to degrees (most-asked conversions):

• 1/12 pitch — 4.76 degrees
• 3/12 pitch — 14.04 degrees
• 4/12 pitch — 18.43 degrees
• 6/12 pitch — 26.57 degrees
• 7/12 pitch — 30.26 degrees (close to 30°)
• 8/12 pitch — 33.69 degrees
• 12/12 pitch — 45.00 degrees

Pitch multiplier for surface area (X/12 pitch):

• 4/12: multiply footprint by 1.054
• 5/12: multiply by 1.083
• 6/12: multiply by 1.118
• 7/12: multiply by 1.158
• 8/12: multiply by 1.202
• 12/12: multiply by 1.414

Common pitches by roof style:

• Modern flat-look — 1/12 to 3/12
• Ranch-style — 3/12 to 5/12
• Bungalow / Craftsman — 4/12 to 6/12
• Cape Cod / Colonial — 6/12 to 8/12
• Victorian / Steep traditional — 8/12 to 12/12
• Chalet / Steep modern — 12/12 and above

These figures get you within rough estimating range. For exact rafter cuts, foundation alignment, and material orders, use the calculator above with your specific measurements.