A Gable Roof Area Calculator is a simple tool designed to help you calculate the total area of a gable roof. A gable roof has two sloping sides that meet at the ridge, forming a triangular shape at each end. Knowing the roof area is essential for tasks like purchasing roofing materials or estimating construction costs.

Formula for Gable Roof Area

The Gable Roof Area is calculated using the following formula:

Roof Area = Roof Length × Roof Width × Slope Multiplier

• Roof Length is the length of the roof from one end to the other.
• Roof Width is the horizontal distance across the roof (from eave to eave).
• Slope Multiplier accounts for the roof's pitch (steepness).

The Slope Multiplier can be calculated using the following formula:

$\text{Slope Multiplier}=\sqrt{1+{\left(\frac{\text{Pitch}}{12}\right)}^2}$

Thus, the complete formula becomes:

$\text{Roof Area}=\text{Roof Length}\times \text{Roof Width}\times \sqrt{1+{\left(\frac{\text{Pitch}}{12}\right)}^2}$

Formula for Roof Pitch

The Roof Pitch represents the slope of the roof, typically expressed as "rise over run" (e.g., a 4:12 pitch means the roof rises 4 units for every 12 horizontal units). The pitch formula is:

$\text{Pitch}=\frac{\text{Rise}}{\text{Run}}$

Where:

• Rise is the vertical distance the roof rises.
• Run is the horizontal distance from the edge of the roof to the ridge.

Formula for Roof Slope

The Roof Slope is the diagonal length from the edge of the roof to the ridge. This forms a right triangle with the rise and run, and you can use the Pythagorean theorem to calculate it.

$\text{Roof Slope}=\sqrt{{\text{Run}}^2+{\text{Rise}}^2}$

Where:

• Run is half of the roof's width.
• Rise is the height of the roof calculated from the pitch.

Formula for Ridge Length

The Ridge Length is the horizontal length of the ridge, which is typically the same as the Roof Length. However, if you have an overhang or need to adjust for any special roof design features, you can adjust accordingly.

For a standard gable roof, the ridge length is equal to the roof length:

$\text{Ridge Length}=\text{Roof Length}$

Formula for Roof Angle

To calculate the Roof Angle in degrees, you can use the arctangent function with the rise and run:

$\text{Roof Angle}=arctan\left(\frac{\text{Rise}}{\text{Run}}\right)\times \left(\frac{180}{\pi }\right)$

This converts the roof angle from radians to degrees.

Example Calculation:

Let's calculate the gable roof area for a roof with the following dimensions:

• Roof Length: 20 feet
• Roof Width: 10 feet
• Roof Pitch: 4:12

First, calculate the slope multiplier:

$\text{Roof Area}=\sqrt{1+{\left(\frac{\text{4}}{12}\right)}^2}$

Slope Multiplier = 1.0541

Now, calculate the roof area:

Roof Area = 20×10×1.0541 = 210.82 square feet

Thus, the gable roof area is 210.82 square feet.