How to Calculate Roof Pitch in Degrees (with 4/12 Example)

While standard pitch ratios (like 6/12) are great for ordering shingles, framers and carpenters need exact angles to cut rafters. If you need to know how to calculate roof pitch in degrees, you have to use a bit of trigonometry: specifically, the inverse tangent (arctangent) function.

The Math Behind Roof Angles

To find the angle of your roof, divide the rise by the run to get a decimal. Then, find the arctangent of that decimal. Most scientific calculators have a button for this (labeled as tan⁻¹ or atan).

How to Calculate a 4/12 Pitch Roof

Let's look at one of the most common residential slopes. If someone asks how to calculate a 4/12 pitch roof into degrees, here is the exact breakdown:

• Step 1: Divide the rise (4) by the run (12). 4 ÷ 12 = 0.3333.
• Step 2: Find the arctangent of 0.3333.
• Result: The angle is exactly 18.43 degrees.

Convert Angles Instantly

If you don't have a scientific calculator on the job site, just use our free Roof Pitch Calculator. Select the "Convert" mode, enter your pitch, and the tool will instantly output your exact framing angle in degrees.