How do you convert roof pitch to degrees?

Take the arctangent of the pitch ratio: for a pitch of rise:12, the angle in degrees is arctan(rise / 12). A 6:12 pitch is arctan(6/12) = arctan(0.5) ≈ 26.57°.

What roof pitch is 45 degrees?

A 45° roof angle corresponds to a 12:12 pitch — equal rise and run — since arctan(12/12) = arctan(1) = 45° exactly.

Is roof pitch the same as roof angle?

No. Pitch is a ratio (rise over a 12-inch run, written like 6:12), while angle is a measurement in degrees. They describe the same slope but aren't numerically interchangeable — a 6:12 pitch is not '6 degrees', it's about 26.6 degrees.

What's a typical residential roof pitch in degrees?

Most residential roofs fall between about 4:12 (roughly 18.4°) and 9:12 (roughly 36.9°), with 6:12 (26.57°) commonly cited as a moderate, walkable-ish slope in many US building guides. Steeper alpine-style roofs can exceed 12:12 (45°).

Guide

Roof pitch to angle in degrees: the conversion table

Roofers specify pitch as rise over a 12-inch run, like 6:12 — not as degrees. Converting requires the arctangent of the ratio, since pitch is a slope, not an angle measurement itself.

By Buğra SözeriPublished September 25, 2026

Roof pitch and roof angle describe the same slope but aren't the same number. Pitch is expressed as a ratio of vertical rise to a fixed 12-inch horizontal run — a "6:12" roof rises 6 inches for every 12 inches it runs horizontally. Angle, by contrast, is a measurement in degrees. Converting from one to the other requires trigonometry, not a simple relabeling.

The formula

The angle in degrees is the arctangent of the rise divided by the run:

angle = arctan(rise / run)

For the standard 12-inch run convention, that's arctan(rise / 12). A 6:12 pitch, for example, works out to arctan(0.5) ≈ 26.57°.

Common roof pitches converted to degrees

Pitch (rise:12)	Angle (degrees)
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°
12:12	45.00°

Notice the relationship isn't linear — doubling the pitch from 6:12 to 12:12 doesn't double the angle from 26.57° to 53.14°, because arctangent is a curved function, not a straight-line ratio. That's a common source of estimation error when someone tries to eyeball a steeper pitch as "twice as steep in degrees."

Why it matters beyond labeling

The angle value, not the pitch ratio, is what feeds into load calculations, snow-shedding design, and truss engineering software — most structural formulas and CAD tools work in degrees or radians internally, even when the roofing industry itself communicates in pitch ratios on site. Framing squares and speed squares typically have both pitch and degree markings for exactly this reason: the tradesperson thinks in pitch, the engineering math needs the angle.

Frequently asked questions

How do you convert roof pitch to degrees?: Take the arctangent of the pitch ratio: for a pitch of rise:12, the angle in degrees is arctan(rise / 12). A 6:12 pitch is arctan(6/12) = arctan(0.5) ≈ 26.57°.
What roof pitch is 45 degrees?: A 45° roof angle corresponds to a 12:12 pitch — equal rise and run — since arctan(12/12) = arctan(1) = 45° exactly.
Is roof pitch the same as roof angle?: No. Pitch is a ratio (rise over a 12-inch run, written like 6:12), while angle is a measurement in degrees. They describe the same slope but aren't numerically interchangeable — a 6:12 pitch is not '6 degrees', it's about 26.6 degrees.
What's a typical residential roof pitch in degrees?: Most residential roofs fall between about 4:12 (roughly 18.4°) and 9:12 (roughly 36.9°), with 6:12 (26.57°) commonly cited as a moderate, walkable-ish slope in many US building guides. Steeper alpine-style roofs can exceed 12:12 (45°).

Sources & references

Authoritative references cited by this piece. Verified by Buğra Sözeri on the dates shown and re-checked at every deploy.

BIPM — SI Brochure, 9th edition (angle and trigonometric definitions) — Reference for the trigonometric relationship (arctangent) used to derive angle from a slope ratio(as of 2026-09-25)