Roof Pitch Calculator
Use this free roof pitch calculator to quickly determine the slope and angle of your roof. Enter values like rise and run to get accurate pitch results, making it easy to plan roofing materials, calculate angles, and estimate construction requirements for residential and DIY projects.
Pitch = rise per 12 inches of run · A 6/12 pitch rises 6 inches for every 12 inches of horizontal run · Roof area always exceeds footprint due to slope
How Does the Roof Pitch Calculator Work?
Roof pitch describes how steeply a roof slopes, expressed as the number of inches of vertical rise per 12 inches of horizontal run. A 6/12 pitch means the roof rises 6 inches for every 12 inches it runs horizontally. This calculator works from three input modes — rise & run, angle in degrees, or pitch notation — and calculates the pitch, angle, pitch multiplier, rafter length, and actual sloped roof area.
Knowing your roof pitch is essential for roofing material calculations. Roof shingles, metal panels, and underlayment are quoted by the actual sloped area — not the flat footprint. A 6/12 pitch roof is 11.8% larger than its footprint; a 12/12 pitch is 41% larger. Skipping the pitch multiplier is how homeowners under-order roofing materials. Use our roofing material calculator for a full shingle and underlayment count once you know your pitch.
You don't need to get on the roof to measure pitch. Place a level horizontally against the roof surface and measure 12 inches along the level. Then measure the vertical distance from the 12-inch mark down to the roof surface — that's your rise. Example: if you measure 5 inches of rise over 12 inches of run, your pitch is 5/12. You can also use a smartphone app with an inclinometer for an instant angle reading from inside the attic.
Roof Pitch Chart — All Common Pitches
| Pitch | Angle | Pitch Multiplier | Category | Common Uses |
|---|---|---|---|---|
| 1/12 | 4.8° | 1.003 | Flat | Low-slope commercial, EPDM membrane |
| 2/12 | 9.5° | 1.014 | Low | Shed roofs, low-slope residential additions |
| 3/12 | 14.0° | 1.031 | Low | Modern homes, flat-look aesthetic |
| 4/12 | 18.4° | 1.054 | Moderate | Most popular residential pitch — good balance |
| 5/12 | 22.6° | 1.083 | Moderate | Traditional ranch homes, most US regions |
| 6/12 | 26.6° | 1.118 | Moderate | Very common — good drainage, walkable |
| 7/12 | 30.3° | 1.158 | Moderate-steep | Colonial style, usable attic space |
| 8/12 | 33.7° | 1.202 | Steep | Cape Cod, Tudor style |
| 9/12 | 36.9° | 1.250 | Steep | Victorian, full attic |
| 10/12 | 39.8° | 1.302 | Steep | Steep traditional, Gothic Revival |
| 12/12 | 45.0° | 1.414 | Very steep | 45° perfect diagonal — dramatic appearance |
Pitch Multiplier & Actual Roof Area
The pitch multiplier converts your roof's flat footprint into the actual sloped surface area. Roofing materials — shingles, metal panels, underlayment, ice-and-water shield — must cover the sloped surface, not the flat footprint. Using footprint area alone will cause you to under-order materials significantly on steeper roofs.
Example: 30 × 40 ft house (1,200 sq ft footprint) with 6/12 pitch:
1,200 × 1.118 = 1,342 sq ft actual roof area
1,342 ÷ 100 = 13.42 squares of roofing material needed
Roofing is sold in "squares" — 1 square = 100 sq ft of actual sloped roof area. Never use floor plan area or footprint to calculate shingle quantities. A 4/12 pitch adds ~5% to your footprint; a 12/12 pitch adds 41%. Use our roofing material calculator to get a complete shingle, underlayment, and ridge cap count based on your actual roof dimensions and pitch.
Pitch & Roofing Material Compatibility Guide
Not every roofing material works at every pitch. Using the wrong material for your pitch leads to leaks, voided warranties, and premature failure.
| Material | Min Pitch | Ideal Pitch Range | Notes |
|---|---|---|---|
| EPDM / TPO Membrane | 0/12 (flat) | 0–2/12 | Commercial flat roofs — requires proper drainage |
| Built-up Roofing (BUR) | 0/12 | 0–3/12 | Gravel-topped, low-slope commercial |
| Modified Bitumen | 0.25/12 | 0–4/12 | Torch-applied low-slope membrane |
| Metal Roofing (standing seam) | 0.5/12 | 0.5/12+ | Works on near-flat to very steep — most versatile |
| Asphalt Shingles (3-tab) | 2/12 | 4–9/12 | Most common — requires 2× underlayment below 4/12 |
| Architectural / Dimensional Shingles | 2/12 | 4–12/12 | Most popular residential — 30–50 year lifespan |
| Wood Shakes / Shingles | 3/12 | 4–12/12 | Requires breathing gap; not for low pitches |
| Slate | 4/12 | 6–12/12 | Heavy — verify structural support; 75–150 yr lifespan |
| Concrete / Clay Tile | 4/12 | 5–12/12 | Very heavy — requires engineered support |
Example Calculations
Example 1 — Finding Pitch from Rise & Run
Pitch = 7/12
Angle = arctan(7 ÷ 12) = 30.3°
Pitch multiplier = √(1 + (7/12)²) = 1.158
Example 2 — Calculating Actual Roof Area
Footprint = 28 × 45 = 1,260 sq ft
Run = 28 ÷ 2 = 14 ft per side
Rafter length = √(14² + 7²) = √(196 + 49) = √245 = 15.65 ft
Actual roof area = 1,260 × 1.118 = 1,409 sq ft = 14.09 squares
Example 3 — Converting Angle to Pitch
Rise = tan(22.6°) × 12 = 0.4163 × 12 = 5 inches → 5/12 pitch
Pitch multiplier = 1.083
Frequently Asked Questions
How We Calculate
Pitch from Rise & Run
Pitch = Rise (inches) ÷ Run (inches)
In the US, roof pitch is always expressed as rise per 12 inches of horizontal run — so a “6/12 pitch” rises 6 inches for every 12 inches of horizontal distance. The run is always 12 by convention when expressing pitch in X/12 notation. Internally the calculator uses the actual ratio Rise÷Run for all trigonometric calculations.
Angle Conversion
Angle = arctan(Rise ÷ Run) — in degrees
The calculator uses JavaScript’s Math.atan(rise/run) function and converts from radians to degrees by multiplying by (180/π). The reverse — converting angle to rise — uses Math.tan(angle × π/180) × 12. A 45° angle corresponds exactly to a 12/12 pitch.
Pitch Multiplier
Pitch Multiplier = √(1 + (Rise÷Run)²)
This is derived from the Pythagorean theorem. For every 12 inches of horizontal run at a given rise, the actual sloped distance along the rafter is √(12² + Rise²) inches. Dividing by 12 gives the ratio of sloped length to horizontal run — the pitch multiplier. A 6/12 pitch multiplier = √(1 + 0.25) = √1.25 = 1.118, meaning the actual roof surface is 11.8% larger than the flat footprint.
Rafter Length
Rafter Length = √(Run² + Rise²) — where Run = Span ÷ 2 (in feet)
The rafter run is half the total roof span (for a symmetrical gable roof). Rise in feet = (rise in inches ÷ 12) × Run in feet. The rafter length is the hypotenuse of the right triangle formed by the run and the rise. This is the structural rafter length before adding eave overhang — add your planned eave overhang (typically 1–2 ft) to the calculated rafter length for your lumber order.
Actual Roof Area
Actual Roof Area = Footprint Area × Pitch Multiplier
The footprint is Span × Length (the plan-view dimensions of the building). For a gable roof, this equals the total sloped area of both roof faces. The pitch multiplier converts the flat footprint to the actual sloped surface area — the quantity used for all roofing material orders. Roofing is sold in “squares” where 1 square = 100 sq ft of actual sloped area, so divide the sloped area by 100 to get the number of squares needed.
- NRCA (National Roofing Contractors Association) — The NRCA Roofing Manual — Roof pitch conventions (rise per 12 inches of run), pitch multiplier methodology, roofing square definition (1 square = 100 sq ft of actual sloped area), and minimum pitch requirements by roofing material type referenced throughout this calculator. The NRCA Roofing Manual is the industry-standard reference for all US roofing contractors. NRCA, current edition.
- IRC 2026 (International Residential Code) — Chapter R9 Roof Assemblies — Minimum roof pitch requirements by material type (asphalt shingles: 2/12 minimum with special installation, 4/12 standard; metal roofing: 0.5/12 minimum; slate and clay tile: 4/12 minimum) referenced in the material compatibility table and FAQ on minimum shingle pitch. Also the source for ice-and-water shield underlayment requirements below 4/12 pitch. International Code Council, 2026 edition.
- AWC (American Wood Council) — Span Tables for Joists and Rafters — Rafter span and length conventions used in the rafter length formula (run = half-span for symmetrical gable roof). The Pythagorean formula for rafter length calculation referenced in the How We Calculate section is the basis of all AWC rafter span tables. Eave overhang addition guidance (1–2 ft typical) follows AWC rafter calculation practice. American Wood Council, current edition.
- Asphalt Roofing Manufacturers Association (ARMA) — Residential Asphalt Roofing Manual — Minimum pitch requirements for 3-tab shingles and architectural/dimensional shingles (2/12 absolute minimum; 4/12 standard for normal installation without special low-slope procedures), double-underlayment requirement below 4/12, and ice-and-water shield specifications. Referenced in the material compatibility guide for asphalt shingles and the FAQ on minimum pitch for shingles. ARMA, current edition.
Minimum pitch requirements shown are general guidelines — always verify with your specific roofing material manufacturer’s installation instructions and local building department requirements, which may be more stringent than IRC minimums. ConstructlyTools does not have a paid relationship with any roofing manufacturer or contractor mentioned on this page.