To determine the roof pitch in degrees, you can use the following formula:
Roof Pitch (in degrees) = arctan(rise / run)
Where:
"rise" is the vertical height or the number of units the roof rises vertically.
"run" is the horizontal length or the number of units the roof extends horizontally.
If you have a roof pitch of 30 degrees, we can find the corresponding rise and run using the formula and some trigonometry.
Let's assume the run is 12 units (typical for the 12/12 pitch notation) to make the calculation easier.
Roof Pitch (in degrees) = 30 degrees (given)
Run = 12 units (assumed)
Now, we can rearrange the formula to solve for the rise:
Rise = run * tan(Roof Pitch in degrees)
Rise = 12 * tan(30 degrees)
Rise ≈ 6.93 units
So, for a roof pitch of 30 degrees and a run of 12 units, the vertical rise is approximately 6.93 units.
Keep in mind that this is a theoretical calculation, and in practical roofing scenarios, the rise and run might be rounded to more convenient measurements based on construction standards and materials.
To convert the roof pitch from degrees to the standard "x/12" notation, you need to determine the rise and run values.
The pitch is defined as the angle between the roof surface and the horizontal plane.
Here's how you can calculate the pitch in the "x/12" format when the roof pitch is 30 degrees.
Convert the degrees to a decimal form: 30 degrees.
Determine the rise and run values:
The rise is the vertical distance from the roof's highest point to the lowest point.
The run is the horizontal distance from the starting point to the ending point.
Use trigonometry to calculate the rise and run:
Given the pitch angle (30 degrees), you can use the tangent function (tan) to find the rise and run.
tan(30 degrees) = rise / run.
Solve for rise and run:
rise = run * tan(30 degrees).
Choose a value for the run (e.g., 12 inches or 12 feet) to determine the corresponding rise value.
For example, let's assume you choose a run of 12 inches:
rise = 12 inches * tan(30 degrees)
rise = 12 inches * 0.57735 (rounded to 5 decimal places)
rise ≈ 6.93 inches
So, a roof with a 30-degree pitch can be expressed as approximately 7/12 (rise of 6.93 inches for every 12 inches of run).
Keep in mind that you can choose a different run value (e.g., 24 inches, 36 inches, etc.) to calculate the corresponding rise.
