Roof Angle Calculator
Calculate roof angle, roof pitch, roof slope, rise, run, and rafter length from your measurements.
Enter Your Measurements
Roof Angle Results
Roof angle is calculated from the vertical rise and horizontal run using the arctangent formula.
How to Use the Roof Angle Calculator
Our free roof angle calculator helps you calculate the angle of a roof from its vertical rise and horizontal run. It also provides related measurements including roof pitch, roof slope, and rafter length.
- Enter the vertical rise of the roof.
- Enter the horizontal run of the roof.
- Select the appropriate unit for each measurement.
- Click Calculate Roof Angle.
- Review the calculated roof angle, pitch, slope, and rafter length.
What Is a Roof Angle?
Roof angle is the angle formed between the roof surface and the horizontal line. It describes how steep or shallow the roof is and is commonly measured in degrees.
For example, a roof with a 6:12 pitch has a roof angle of approximately 26.57 degrees. A steeper roof has a larger angle, while a shallower roof has a smaller angle.
Roof Angle Formula
The roof angle can be calculated using the vertical rise and horizontal run of the roof.
Roof Angle = arctan(Rise ÷ Run)
The result is converted from radians to degrees. For example, if the rise is 6 feet and the run is 12 feet:
arctan(6 ÷ 12) ≈ 26.57°
What Does This Roof Angle Calculator Calculate?
This calculator provides several related roof measurements based on the rise and run you enter.
- Roof Angle: The angle of the roof measured from the horizontal in degrees.
- Roof Pitch: The amount of vertical rise for every 12 inches of horizontal run.
- Roof Slope: The roof slope expressed as a percentage.
- Rise: The vertical measurement entered for the roof.
- Run: The horizontal measurement entered for the roof.
- Rafter Length: The diagonal distance calculated from the rise and run.
Roof Angle Example
Suppose a roof has a vertical rise of 6 feet and a horizontal run of 12 feet.
Using the roof angle formula:
arctan(6 ÷ 12) ≈ 26.57°
Therefore, the roof angle is approximately 26.57 degrees. These measurements also correspond to a 6:12 roof pitch and a 50% roof slope.
The corresponding rafter length is approximately 13 feet 5 inches.
Roof Angle vs. Roof Pitch
Roof angle and roof pitch describe the steepness of a roof in different ways. Roof angle is normally expressed in degrees, while roof pitch is commonly expressed as a rise-over-12 ratio.
For example, a 6:12 roof pitch corresponds to a roof angle of approximately 26.57 degrees. Both measurements describe the same basic roof geometry.
Common Roof Pitch and Angle Values
Different roof pitches produce different roof angles. The following examples show the approximate relationship between common roof pitches and their corresponding angles.
- 2:12 — approximately 9.46°
- 3:12 — approximately 14.04°
- 4:12 — approximately 18.43°
- 5:12 — approximately 22.62°
- 6:12 — approximately 26.57°
- 8:12 — approximately 33.69°
- 10:12 — approximately 39.81°
- 12:12 — 45°
How Roof Angle Relates to Rafter Length
Roof angle affects the length of a rafter because the angle determines the relationship between the horizontal run and vertical rise.
For the same horizontal run, a steeper roof angle produces a greater vertical rise and therefore a longer rafter.
A shallower roof angle produces a smaller rise and a shorter rafter for the same horizontal run.
For detailed rafter measurements, use our Rafter Calculator.
Roof Angle Measurements and Units
This calculator allows you to enter rise and run measurements using feet, inches, meters, or centimeters.
The rise and run should describe the same section of the roof. Using accurate and consistent measurements helps produce reliable mathematical results.
Frequently Asked Questions
How do you calculate roof angle?
Roof angle can be calculated using the inverse tangent of the vertical rise divided by the horizontal run. The result is expressed in degrees.
What angle is a 6:12 roof pitch?
A 6:12 roof pitch has a roof angle of approximately 26.57 degrees.
What is the difference between roof angle and roof pitch?
Roof angle is expressed in degrees, while roof pitch is commonly expressed as a rise-over-12 ratio. For example, a 6:12 pitch corresponds to approximately 26.57 degrees.
Does roof angle affect rafter length?
Yes. For the same horizontal run, a steeper roof angle produces a greater rise and therefore a longer rafter.
Can I calculate roof pitch from roof angle?
Yes. Roof angle and roof pitch are mathematically related. This calculator calculates both values from the rise and run measurements you enter.
Important Information
The results provided by this calculator are mathematical estimates based on the measurements entered by the user. Actual roof construction can involve additional factors such as framing methods, structural loads, lumber dimensions, roofing materials, local building codes, and design requirements.
Always verify measurements and construction requirements before using calculator results for actual building work. Consult applicable building codes and a qualified professional when structural decisions are involved.
Related Calculators
Explore our other roofing calculators to calculate rafter dimensions, roof pitch, and roof slope.
Calculate Your Roof Angle
Enter your roof rise and run above to calculate roof angle, roof pitch, roof slope, and rafter length.