Roof Angle Calculator
Calculate the roof angle in degrees and radians from rise and run measurements.
Formula & Explanation
The roof angle is calculated using the arctangent (inverse tangent) function: Angle (degrees) = arctan(Rise ÷ Run) × (180 ÷ π) Angle (radians) = arctan(Rise ÷ Run) For a 6:12 roof (6 feet rise over 12 feet run), the angle is arctan(6÷12) = arctan(0.5) = 26.57 degrees or 0.464 radians. This calculation converts pitch measurements into angle format, which is useful for structural engineering calculations and compatibility with certain roofing materials.
Assumptions
- •Rise and run are measured in the same units
- •Angle is measured from horizontal (0° = flat, 90° = vertical)
- •For residential roofing, typical angles range from 18° to 45°
Example Calculation
A 6:12 pitch has an angle of approximately 26.57 degrees or 0.4636 radians from horizontal.
Inputs
Results
Common Pitch Angles
| pitch | angle |
|---|---|
| 3:12 | 14.04° |
| 4:12 | 18.43° |
| 5:12 | 22.62° |
| 6:12 | 26.57° |
| 8:12 | 33.69° |
| 12:12 | 45.00° |
Frequently Asked Questions
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