4/12 Pitch Roof Calculator

The 4/12 Pitch Roof Calculator determines missing roof dimensions like rafter length, roof span, or roof pitch angle when two of the values are provided.

This calculator is designed for builders, architects, and homeowners to simplify roof design calculations. It works by using trigonometric relationships to compute the required values based on the classic 4/12 pitch angle standard.

Enter any two values—such as the rafter length, roof span, or roof pitch angle—and the calculator will compute the third.

Formula

Rafter Length:

\text{Rafter Length} = \frac{\text{Roof Span}}{\cos(\text{Pitch Angle})}

Roof Span:

\text{Roof Span} = \text{Rafter Length} \times \cos(\text{Pitch Angle})

Roof Pitch Angle:

\text{Pitch Angle (in degrees)} = \arccos\left(\frac{\text{Roof Span}}{\text{Rafter Length}}\right) \times \frac{180}{\pi}

Variable	Description	Units
Rafter Length	Length of the rafter	ft or m
Roof Span	Horizontal span of the roof	ft or m
Pitch Angle	Angle of the roof’s pitch	degrees

Solved Calculations

Example 1: Calculate Rafter Length

Input:
- Roof Span = $15 \, \text{f$
- Pitch Angle = $18$

Step	Formula	Result
Convert Pitch Angle to Radians	$\text{Radians} = 18.43 \times$	$0.3216 \, \text{ra$
Calculate Rafter Length	$\text{Rafter} = \frac{\text{Span}}{\cos(\tex$	$15 / \cos(0.3216) = 15.6$

Example 2: Calculate Pitch Angle

Input:
- Roof Span = $12 \, \$
- Rafter Length = $13.2 \$

Step	Formula	Result
Calculate Pitch Angle (Radians)	$\text{Angle} = \arccos(\text{Span} / \text$	$\arccos(12 / 13.2) = 0.3041 \, \t$
Convert to Degrees	$\text{Degrees} = 0.3041 \times$	$17.4$

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