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Roof Pitch Calculator
Convert roof slope between rise and run, X : 12 pitch, degrees and percent slope — and get the pitch multiplier, rise per foot and geometric sloped length from the same shared roof geometry engine used across the BuildCalcWorks roofing calculators.
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Roof pitch result
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Enter a rise and run, an x : 12 pitch, an angle or a percent slope, then select Calculate to convert between all of them and see the pitch multiplier.
Roof work and direct roof measurement can involve fall hazards. Use plans, safe measurement methods, or qualified professionals where appropriate.
Roof Pitch Conversion Table
Every value is generated from the shared conversion formulas — arctan(rise ÷ 12) for the angle and √(1 + (rise ÷ 12)²) for the multiplier. Reference values only; no pitch is recommended.
| X:12 pitch | Degrees | Percent | Multiplier |
|---|---|---|---|
| 0:12 | 0° | 0% | 1.0000 |
| 0.5:12 | ≈ 2.39° | 4.17% | 1.0009 |
| 1:12 | ≈ 4.76° | 8.33% | 1.0035 |
| 2:12 | ≈ 9.46° | 16.67% | 1.0138 |
| 3:12 | ≈ 14.04° | 25% | 1.0308 |
| 4:12 | ≈ 18.43° | 33.33% | 1.0541 |
| 5:12 | ≈ 22.62° | 41.67% | 1.0833 |
| 6:12 | ≈ 26.57° | 50% | 1.1180 |
| 7:12 | ≈ 30.26° | 58.33% | 1.1577 |
| 8:12 | ≈ 33.69° | 66.67% | 1.2019 |
| 9:12 | ≈ 36.87° | 75% | 1.2500 |
| 10:12 | ≈ 39.81° | 83.33% | 1.3017 |
| 11:12 | ≈ 42.51° | 91.67% | 1.3566 |
| 12:12 | ≈ 45.00° | 100% | 1.4142 |
| 14:12 | ≈ 49.40° | 116.67% | 1.5366 |
| 16:12 | ≈ 53.13° | 133.33% | 1.6667 |
| 18:12 | ≈ 56.31° | 150% | 1.8028 |
| 21:12 | ≈ 60.26° | 175% | 2.0156 |
In everyday roofing use, “roof pitch” and “roof slope” are often used interchangeably. BuildCalcWorks uses the common X:12 rise-to-horizontal-run convention.
How Do I Calculate Roof Pitch?
Roof pitch, or roof slope, is the ratio of vertical rise to horizontal run. In U.S. roofing it is commonly written as X : 12.
Slope Decimal = Rise ÷ Run
X = (Rise ÷ Run) × 12
6 in rise ÷ 12 in run = 0.5 → 6:12
A roof that rises 6 inches for every 12 inches of horizontal run is a 6:12 roof. The NRCA describes roof slope using this same rise-to-horizontal-run relationship, and current GAF roofing guidance uses the rise/run definition as well.
The run is the horizontal distance only — never the sloped rafter line. Rise and run can be entered in different units here, because they are converted to a common unit before dividing.
How to Convert Roof Pitch to Degrees
Angle = arctan(Rise ÷ Run)
6:12 → arctan(0.5) ≈ 26.57°
4:12 → ≈ 18.43°
How to Convert Degrees to Roof Pitch
X = tan(Angle) × 12
45° → tan(45°) = 1 → 1 × 12 = 12:12
30° → ≈ 6.93:12
An angle of exactly 90° has no defined slope, because the tangent is undefined there, so the calculator accepts angles below 90° only.
Roof Pitch to Percent Slope
Slope % = Rise ÷ Run × 100
3:12 = 25% · 6:12 = 50% · 12:12 = 100%
X = (Percent ÷ 100) × 12 → 50% → 6:12
Percent slope can exceed 100%. A 100% slope is 45°, and steeper roofs — such as 18:12 at 150% and ≈ 56.31° — are mathematically valid and fully supported.
Roof Pitch Multiplier
The pitch multiplier is the ratio between sloped length and horizontal run.
Multiplier = √(1 + Slope²) = 1 ÷ cos(Angle)
6:12 → √(1 + 0.5²) = 1.1180
12:12 → √2 = 1.4142
It converts a horizontal run into a sloped length, and a horizontal footprint area into sloped roof surface area. This is the same multiplier the Roof Square Footage Calculator and the Roofing Calculator use — BuildCalcWorks keeps one shared pitch engine so the values can never disagree.
Using Roof Pitch to Calculate Roof Area
Sloped Area = Horizontal Area × Pitch Multiplier
1,000 sq ft footprint at 6:12 × 1.118 ≈ 1,118 sq ft roof surface
Roof area itself is calculated on its own page — this calculator gives you the multiplier and the conversions.
Roof Square Footage CalculatorUsing Pitch to Estimate Sloped Length
Sloped Length = Horizontal Run × Pitch Multiplier = √(Rise² + Run²)
10 ft run at 6:12 → rise 5 ft → √(10² + 5²) ≈ 11.1803 ft
Geometric length only. This does not determine required rafter size, span, bearing, overhang, ridge connection or structural suitability. It does not calculate required rafter dimensions, structural span, birdsmouth cuts, ridge details or overhang details.
Roof Pitch vs. Roof Slope
In common construction usage, roof pitch and roof slope are often used interchangeably to describe roof steepness. Technical references may distinguish the terms: the NRCA defines roof slope by rise over horizontal run, while GAF's professional field guide notes a technical distinction between slope (rise relative to horizontal run) and pitch (rise relative to total span), and also notes that "slope" is the term commonly used in the field.
In everyday roofing use, “roof pitch” and “roof slope” are often used interchangeably. BuildCalcWorks uses the common X:12 rise-to-horizontal-run convention.
This calculator converts measurements. It does not classify roofs into categories such as "conventional" or "flat", because manufacturers and industry references use varying categories, and it does not infer whether a particular roofing product suits a given slope — products have their own minimum slopes, underlayment requirements, manufacturer instructions and code requirements.
How Roof Pitch Is Measured
Pitch compares vertical rise with horizontal run: 6 inches of rise over 12 inches of horizontal run is 6:12. Any consistent pair of rise and run measurements gives the same slope.
Roof work and direct roof measurement can involve fall hazards. Use plans, safe measurement methods, or qualified professionals where appropriate.
- Building plans, drawings or architectural documents
- Framing or attic measurements where they are safely accessible
- Existing construction documentation or a previous roofing quote
- Digital or aerial roof measurement reports
- A qualified roofing professional
Disclaimer: Geometry and conversion tool only. This calculator does not determine structural rafter sizing, roofing-system suitability or code compliance. Read full Disclaimer.
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