What is roof pitch?
Roof pitch describes how steep a roof is. It is the ratio of the vertical rise to the horizontal run. In construction it is usually written as "x-in-12" — meaning the roof rises x inches for every 12 inches of horizontal distance. A 6-in-12 roof, for example, rises 6 inches over each foot of run. This calculator converts any rise and run into the pitch angle (degrees), the standard rise-per-12 ratio, the slope percentage, and the rafter length.
How to use it
Enter the vertical rise and the horizontal run in the same units (inches work well). The calculator returns the pitch angle, the x-in-12 ratio, the slope as a percentage, and the rafter (hypotenuse) length per the rise and run you entered. You can measure rise and run directly with a level and tape, or read them from architectural drawings.
The formula explained
The pitch angle is the inverse tangent of rise divided by run: angle = arctan(rise / run). The familiar building ratio normalizes the run to 12: pitch = (rise / run) × 12. The slope percentage is simply (rise / run) × 100, and the rafter length follows the Pythagorean theorem: √(rise² + run²).
$$\begin{gathered} \theta = \arctan\!\left(\dfrac{\text{Rise}}{\text{Run}}\right) \\[1.5em] \text{where}\quad \left\{ \begin{aligned} \text{Pitch} &= \dfrac{\text{Rise}}{\text{Run}} \times 12 \\ \text{Slope}\,\% &= \dfrac{\text{Rise}}{\text{Run}} \times 100 \\ \text{Rafter} &= \sqrt{\text{Rise}^{2} + \text{Run}^{2}} \end{aligned} \right. \end{gathered}$$
Worked example
Suppose a roof rises 6 inches over a run of 12 inches. The angle is arctan(6/12) = arctan(0.5) ≈ 26.57°. The pitch ratio is (6/12) × 12 = 6, so it is a 6-in-12 roof. The slope is 50%, and the rafter length is √(6² + 12²) = √180 ≈ 13.42 inches per foot of run.
$$\theta = \arctan\!\left(\frac{6}{12}\right) = \arctan(0.5) \approx 26.57°$$$$\text{Pitch} = \left(\frac{6}{12}\right) \times 12 = 6$$$$\text{Rafter} = \sqrt{6^{2} + 12^{2}} = \sqrt{180} \approx 13.42$$FAQ
Is pitch the same as slope? Roughly — pitch usually refers to the x-in-12 ratio, while slope is often the percentage or the angle. This tool gives all three.
What units should I use? Use any consistent unit for rise and run; the ratio, percentage, and angle are unit-independent. The rafter length comes out in whatever unit you used.
What is a common roof pitch? Residential roofs commonly range from 4-in-12 to 9-in-12. Below 2-in-12 is considered low-slope or flat.
