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Roof Pitch to Angle Calculator

Convert a roof pitch expressed as rise over run (e.g. 6:12) to the equivalent angle in degrees using the inverse tangent.

Pitch to angle
Enter rise and run (typically rise and 12 for standard X:12 pitch notation).
Pitch dimensions
in

Vertical inches of rise. For standard notation, this is X in X:12 pitch (e.g. 6 for a 6:12 pitch).

in

Horizontal inches of run. In standard US roofing notation, run is always 12. Change only if using a different run base.

Angle (degrees)

26.57 deg

Pitch (in per ft): 6 in per ft

What is roof pitch, and when do you need the angle in degrees?

Pitch is the rise-over-run ratio used in U.S. framing; degrees are used for tools, tables, and energy analysis.

Roof pitch describes how steeply a roof slopes. In the United States, pitch is expressed as rise per 12 inches of horizontal run: a 6:12 pitch rises 6 inches for every foot of run. The 12-run convention allows a framing square to be used directly for layout, and pitch tables for rafters and snow loads are built around this standard.

Degrees express the same slope as an angle measured from horizontal. Tools like circular saws and bevel gauges are set in degrees. Solar installation tilt tables, some snow-load calculations, and energy analysis software specify roof slope in degrees rather than pitch notation. The conversion is straightforward: angle in degrees = inverse tangent of the rise-to-run ratio, converted from radians to degrees.

Common reference points: a 4:12 pitch is about 18.4 degrees (shallow), a 6:12 pitch is about 26.6 degrees (moderate), a 12:12 pitch is exactly 45 degrees. Roofs above 7:12 (about 30 degrees) are considered steep slope under most roofing material standards and require additional safety precautions during construction.

How to convert roof pitch to angle in degrees

The inverse tangent formula, radians to degrees, and standard pitch reference values.

Formula

angle (degrees) = atan(rise / run) x (180 / pi)

How the formula works

Angle in degrees = atan(rise / run) x (180 / pi). The inverse tangent (atan) of the rise-to-run ratio gives the angle in radians. Multiplying by 180 / pi converts radians to degrees. For a standard X:12 pitch, rise = X and run = 12. The calculator also outputs the pitch in inches per foot (rise / run x 12), which is the same as the rise value when run = 12.

Standard X:12 notation

Enter the rise and run that match your pitch notation. For a 6:12 pitch, enter rise = 6 and run = 12. For a 4:12 pitch, enter rise = 4 and run = 12. If your pitch is expressed differently (for example, 1:3 meaning 4 inches of rise per 12 inches of run), enter those values directly and the formula still applies.

Reference values

Pitch Degrees
2:12 9.46
4:12 18.43
6:12 26.57
8:12 33.69
10:12 39.81
12:12 45.00

Rounding

Degrees are shown to two decimal places. For saw blade settings, round to the nearest half degree or the nearest graduation on your tool.

Example

A 6:12 pitch (rise = 6, run = 12):
  1. 1
    Slope ratio6 / 12 = 0.5
  2. 2
    Inverse tangentatan(0.5) = 0.4636 radians
  3. 3
    Convert to degrees0.4636 x (180 / pi) = 26.57 degrees
Result26.57 degrees

FAQ

What does X:12 pitch mean?

In U.S. roofing, pitch is expressed as rise per 12 inches of horizontal run. A 6:12 pitch rises 6 inches for every 12 inches of horizontal run. The 12-inch run base is a convention that makes pitches easy to compare and lay out with a framing square. A 12:12 pitch is a 45-degree slope; a 4:12 pitch is a gentle slope common on ranches; a 10:12 pitch is steep and requires additional safety precautions.

When would I need the angle in degrees instead of pitch?

Degrees are used when working with materials or tools that specify angles rather than rise:run ratios. Bevel cuts on rafters, saw blade settings, and some ventilation and snow-load tables reference degrees. Solar panel installation often specifies tilt in degrees rather than roofing pitch. Structural engineering calculations and some energy-analysis software also use degrees.

What pitch is considered steep or low slope?

Low-slope roofs are generally below 2:12 (about 9.5 degrees); they require special roofing systems. Conventional shingle roofing starts at about 3:12 to 4:12 (14 to 18 degrees). Steep roofs are above 7:12 (30 degrees) and require fall-protection measures under OSHA 1926.502 during construction. Some material manufacturers restrict their warranties above certain pitches; check product specifications.

What if my rise-and-run is not based on 12?

Enter the actual rise and run values you have. The calculator uses atan(rise / run) and works for any consistent unit pair. For example, a slope of 0.3 meters rise per 1 meter run would be entered as rise = 0.3, run = 1, giving about 16.7 degrees. The 12-run convention is U.S. specific; metric countries often express pitch as a ratio or percentage gradient.

Sources

High-trust standards and documented references.

  1. 1. Handbook 44 (HB 44): Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices

    National Institute of Standards and Technology (NIST)

    NIST HB 44 is cited for its definitions of measurement units and conversion factors; the degree-radian relationship is a standard trigonometric identity.

    https://www.nist.gov/pml/weights-and-measures/publications/nist-handbooks/hb44

  2. 2. International Residential Code (IRC), Chapter 8: Roof-Ceiling Construction

    International Code Council

    IRC Chapter 8 references roof pitch in design tables for rafters and ceiling joists; standard framing practice and pitch definitions are established here.

    https://codes.iccsafe.org/content/IRC2021P1/chapter-8-roof-ceiling-construction