What is roof pitch?
Roof pitch describes how steep a roof is. It is most often expressed as a ratio of vertical rise to horizontal run — for example, a "6-in-12" roof rises 6 units for every 12 units of horizontal distance. This calculator converts any rise and run into the roof's angle in degrees, its equivalent x-in-12 pitch, the slope (hypotenuse) length, and the slope percentage.
How to use it
Enter the rise (vertical height) and the run (horizontal distance) in any consistent unit — inches, feet, centimetres, it does not matter as long as both use the same unit. The pitch angle and slope percentage are unit-free; the slope length is returned in the same unit you entered.
The formula explained
The angle comes from basic trigonometry: \(\theta = \arctan\!\left(\frac{\text{Rise}}{\text{Run}}\right)\). Because rise and run form the two legs of a right triangle, the slope length is the hypotenuse:
$$\text{Slope} = \sqrt{\text{Rise}^{2} + \text{Run}^{2}}$$The familiar x-in-12 pitch is simply \(\text{Pitch} = \frac{\text{Rise}}{\text{Run}} \times 12\), and slope percentage is \(\text{Slope \%} = \frac{\text{Rise}}{\text{Run}} \times 100\%\).
Worked example
For a roof with a rise of 6 and a run of 12: the angle is
$$\theta = \arctan\!\left(\frac{6}{12}\right) = \arctan(0.5) \approx 26.57°$$The slope length is
$$\text{Slope} = \sqrt{6^{2} + 12^{2}} = \sqrt{180} \approx 13.416$$The pitch is \(\frac{6}{12} \times 12 = \textbf{6-in-12}\) and the slope percentage is \(50\%\).
FAQ
Is 6-in-12 a steep roof? It is a common, moderate pitch (about 26.6°). Pitches above 9-in-12 are considered steep.
What units should I use? Any unit works for the angle and percentage; just keep rise and run in the same unit. The slope length is returned in that same unit.
Can I use this for a wheelchair ramp? Yes — the slope percentage output is the standard way ramp grades are specified.
