1. How to Convert Roof Pitch to Degrees (θ)
Because vertical rise and horizontal run form the two legs of a right triangle, the pitch angle (θ) at the eave is calculated using the inverse tangent function (arctan or tan-1):
Angle (°) = arctan(Rise ÷ Run) × (180 ÷ π)
Or simply: Angle (°) = arctan(X ÷ 12) in degree mode
Step-by-Step Calculation for a 6:12 Pitch:
- Divide rise by run:
6 ÷ 12 = 0.50. - Take the inverse tangent:
arctan(0.50) ≈ 0.4636 radians. - Convert radians to degrees:
0.4636 × (180 / π) = 26.565°. - Round to standard precision: 26.57°.
2. How to Convert Roof Pitch to Slope Percentage (Grade)
Civil engineers, municipal drainage inspectors, and civil grading plans frequently express incline as a percentage grade. Percentage grade describes the vertical elevation gained per 100 units of horizontal run:
Slope % = (Rise ÷ Run) × 100 = (X ÷ 12) × 100
For example:
- 3:12 Pitch:
(3 ÷ 12) × 100 = 25.00% grade - 6:12 Pitch:
(6 ÷ 12) × 100 = 50.00% grade - 12:12 Pitch:
(12 ÷ 12) × 100 = 100.00% grade
3. Converting Degrees Back to a Pitch Ratio (X:12)
If you have taken an angle reading with a digital inclinometer or smartphone app and need to determine the lumber pitch ratio for ordering rafters:
Rise X = tan(Angle in Degrees) × 12
Example: If your digital level indicates an angle of 30.26°:
tan(30.26°) = 0.5834
Rise X = 0.5834 × 12 = 7.0008 inches
→ Exactly 7:12 Pitch
4. Quick Pitch, Degree & Slope Reference Matrix
| Pitch (X:12) | Degrees (°) | Slope Grade | Pitch Factor | Classification |
|---|---|---|---|---|
| 1:12 | 4.76° | 8.33% | 1.0035 | Low Slope |
| 2:12 | 9.46° | 16.67% | 1.0138 | IRC Threshold |
| 3:12 | 14.04° | 25.00% | 1.0308 | Low Pitch |
| 4:12 | 18.43° | 33.33% | 1.0541 | Standard Conv. |
| 5:12 | 22.62° | 41.67% | 1.0833 | Walkable |
| 6:12 | 26.57° | 50.00% | 1.1180 | Standard Residential |
| 7:12 | 30.26° | 58.33% | 1.1577 | Cape Cod |
| 8:12 | 33.69° | 66.67% | 1.2019 | Steep Transition |
| 9:12 | 36.87° | 75.00% | 1.2500 | Colonial |
| 10:12 | 39.81° | 83.33% | 1.3017 | Harness Mandatory |
| 12:12 | 45.00° | 100.00% | 1.4142 | True 45° Angle |