Roof Pitch Calculator Formula
Understand the math behind the roof pitch calculator. Each variable explained with a worked example.
Formulas Used
Pitch (X/12)
pitch_notation = rise * 12 / runAngle (Degrees)
angle_degrees = (180 / 3.14159) * (rise / run > 0 ? (rise / run - pow(rise / run, 3) / 3 + pow(rise / run, 5) / 5) : 0)Pitch Factor (Multiplier)
pitch_factor = sqrt(1 + pow(rise / run, 2))Slope (%)
slope_percent = rise / run * 100Variables
| Variable | Description | Default |
|---|---|---|
rise | Rise(inches) | 6 |
run | Run(inches) | 12 |
slope_ratio | Derived value= rise / run | calculated |
How It Works
How to Calculate Roof Pitch
Formula
Pitch = Rise / Run (typically expressed as X:12)
Angle = arctan(Rise / Run) in degrees
Pitch Factor = sqrt(1 + (Rise/Run)²)
Roof pitch is expressed as the number of inches of rise per 12 inches of horizontal run. For example, a 6/12 pitch rises 6 inches for every 12 inches of run. The pitch factor is used to convert footprint area to actual roof area.
Worked Example
A roof with 6 inches of rise per 12 inches of run (6/12 pitch).
- 01Pitch = 6/12
- 02Angle = arctan(6/12) = arctan(0.5) = 26.6 degrees
- 03Pitch factor = sqrt(1 + 0.5²) = sqrt(1.25) = 1.1180
- 04Slope = 0.5 × 100 = 50%
Frequently Asked Questions
What is the most common roof pitch?
The most common residential roof pitches are 4/12 to 9/12. A 4/12 pitch is the minimum for asphalt shingles. A 6/12 pitch is considered standard.
What is the pitch factor used for?
Multiply the building footprint area by the pitch factor to get the actual roof surface area. For example, a 1,000 sq ft footprint with a 6/12 pitch: 1,000 × 1.118 = 1,118 sq ft of roof.
What roof pitch is walkable?
Pitches of 6/12 and below are generally considered walkable. From 7/12 to 10/12, roof jacks and harnesses are recommended. Above 10/12 requires specialized equipment.
Learn More
Guide
How to Calculate Roofing Materials: Shingles, Underlayment, and More
Learn how to calculate roofing materials including shingles, underlayment, flashing, and ridge caps. Covers roof area measurement, pitch factors, and waste allowances.
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Open Roof Pitch Calculator