How to Calculate Roof Pitch in Degrees: Formula & Examples

Most roofing conversations use the familiar X:12 notation — a 6:12 pitch, a 4:12 pitch — but there are plenty of situations where you need the roof angle expressed in degrees instead. Rafter cutting tools, digital inclinometers, architectural drawing programs, and solar installation software all work in degrees. Converting between the two systems takes nothing more than a basic formula, and once you see the pattern, it sticks quickly.

Why Degrees Matter in Roofing

The X:12 notation is intuitive for framers and roofers who think in inches per foot. But other trades and tools expect degrees:

Speed squares and digital angle gauges — used when making rafter cuts at the ridge or bird's mouth, both of which are set in degrees.
Architectural drawings — many plans label roof slopes in degrees alongside or instead of X:12 notation.
Solar panel installations — panel tilt calculations and solar irradiance tables are always expressed in degrees from horizontal.
Building permits in some jurisdictions — certain code references (especially international codes) specify minimum roof angles in degrees.
Smartphone inclinometer apps — they read the phone's accelerometer and report an angle in degrees, so you need to know what that number means for your pitch.

Knowing how to convert gives you fluency in both systems and prevents costly errors when switching between them.

The Conversion Formula: Roof Pitch to Degrees

The conversion relies on the arctangent (inverse tangent) function from trigonometry. The formula is:

Degrees = atan(pitch ÷ 12) × (180 ÷ π)

Breaking it down:

pitch is the rise — the X value in your X:12 ratio. For a 6:12 roof, pitch = 6.
atan(pitch ÷ 12) computes the inverse tangent of the rise-to-run ratio, returning the angle in radians.
× (180 ÷ π) converts radians to degrees (since most people — and most calculators in "degree mode" — want the answer in degrees, not radians).

If your calculator is already set to degree mode, the formula simplifies to:

Degrees = atan(pitch ÷ 12)

Just confirm which mode your calculator is in before you start.

Step-by-Step Example: Converting 6:12 to Degrees

Given: 6:12 pitch (rises 6 inches for every 12 inches of run)

Divide the rise by the run: 6 ÷ 12 = 0.5
Apply the arctangent: atan(0.5) = 0.4636 radians
Convert radians to degrees: 0.4636 × (180 ÷ π) = 0.4636 × 57.296 = 26.57°

A 6:12 pitch equals approximately 26.57 degrees.

Two More Quick Examples

4:12 pitch:

4 ÷ 12 = 0.3333
atan(0.3333) = 0.3217 radians
0.3217 × 57.296 = 18.43°

12:12 pitch:

12 ÷ 12 = 1.0
atan(1.0) = 0.7854 radians
0.7854 × 57.296 = 45.00°

The 12:12 result confirms the intuition — a roof that rises exactly as much as it runs horizontally is, in fact, a perfect 45-degree angle.

The Reverse Formula: Converting Degrees Back to Pitch

Need to go the other direction? If you have the angle in degrees and want the X:12 pitch:

Pitch = tan(degrees × π ÷ 180) × 12

Or in degree-mode:

Pitch = tan(degrees) × 12

Example: You measure a 30-degree angle with an inclinometer.

tan(30°) = 0.5774
0.5774 × 12 = 6.93
The nearest standard pitch is approximately 7:12.

Quick-Reference Conversion Table

Use this table to look up common pitches without any calculation:

| Pitch (X:12) | Angle (degrees) | |:---:|:---:| | 1:12 | 4.76° | | 2:12 | 9.46° | | 3:12 | 14.04° | | 4:12 | 18.43° | | 5:12 | 22.62° | | 6:12 | 26.57° | | 7:12 | 30.26° | | 8:12 | 33.69° | | 9:12 | 36.87° | | 10:12 | 39.81° | | 11:12 | 42.51° | | 12:12 | 45.00° | | 13:12 | 47.29° | | 14:12 | 49.40° | | 15:12 | 51.34° | | 16:12 | 53.13° |

All values are rounded to two decimal places.

Using a Calculator or Smartphone

Scientific Calculator

Most scientific calculators have an atan (or tan⁻¹) button. Before you use it:

Put the calculator in degree mode (look for a DEG or D label in the display).
Enter the pitch value, divide by 12, then press atan (or inv + tan on older models).
Read the result — it is already in degrees.

If your calculator is in radian mode, multiply the result by 57.2958 to convert.

Smartphone

The iPhone Calculator app supports atan in scientific mode — rotate the phone to landscape to access it. Android's built-in calculator works the same way. Both default to degree output when in degree mode.

Alternatively, type the expression directly into a Google search bar. Entering atan(6/12) in degrees returns the answer instantly.

The Easiest Method

Skip the arithmetic entirely and use the free Roof Pitch Calculator. Enter your rise and run (or any two known measurements), and it returns the pitch in both X:12 notation and degrees simultaneously.

When Do You Need Degrees vs. X:12 Notation?

Choosing the right format depends on what you are doing:

Use X:12 notation when:

Ordering roofing materials (shingles, tiles, underlayment)
Discussing pitch with a roofing contractor
Checking material compatibility charts
Reading residential building codes in the United States

Use degrees when:

Setting a speed square or digital bevel gauge for rafter cuts
Programming angle cuts into a miter saw
Specifying roof tilt for solar panel mounting calculations
Working from architectural drawings that use degree notation
Measuring an existing roof with a smartphone inclinometer app

The two systems measure the same thing — the steepness of the slope — from different mathematical perspectives. Knowing both means you can work with any tool, drawing, or code reference without stopping to convert by hand every time.

Key Takeaways

The conversion formula is Degrees = atan(pitch ÷ 12) × (180 ÷ π), or simply atan(pitch ÷ 12) if your calculator is in degree mode.
A 6:12 pitch = 26.57°, a 4:12 pitch = 18.43°, and a 12:12 pitch = 45.00° exactly.
To reverse the conversion: Pitch = tan(degrees) × 12.
Degrees are essential for speed squares, rafter cuts, solar installations, and some architectural drawings.
The Roof Pitch Calculator converts between X:12 and degrees automatically — no formula required.