Roof Pitch to Degrees: Full Conversion Chart and Formula

The conversion formula

A roof plane is a right triangle. The run is the adjacent side, the rise is the opposite side, and the rafter is the hypotenuse. The tangent of the roof angle is therefore opposite over adjacent — rise over run — and the angle itself is the inverse tangent of that ratio.

Because American pitch notation already fixes the run at 12, you can drop the run entirely: a 7:12 roof is arctan(7 ÷ 12) = arctan(0.5833) = 30.26 degrees. Make sure your calculator is in degree mode rather than radians; a result of 0.528 means you are reading radians and need to multiply by 180/π.

Percent grade uses the same ratio without the arctangent: (rise ÷ run) × 100. This is why the three notations diverge. On a 6:12 roof the ratio is 0.5, so the grade is 50 percent while the angle is 26.57 degrees. Nothing about the roof changed — only the way the same ratio was reported.

Roof pitch to degrees chart (1:12 to 24:12)

The area multiplier is √(rise² + run²) ÷ run — the factor that converts a plan-view footprint into true sloped area. The hip/valley factor is √(rise² + 2·run²) ÷ run and applies only to the diagonal members that run at 45 degrees in plan.

Half and quarter steps

Low-slope roofs are routinely specified in quarter-inch increments because building codes set drainage minimums there. These are the values you need when a spec sheet says "minimum 1/4 inch per foot":

A quarter inch per foot — 1/4:12 — is the classic minimum drainage slope for a built-up or single-ply membrane roof, and it is barely over one degree. Gutters use an even flatter fall, typically 1/16 to 1/8 inch per foot, which is why a gutter that looks dead level to the eye can still drain correctly.

Converting degrees back to pitch

Architects, solar designers and anyone working in metric usually hold an angle and need a framing pitch. Multiply the tangent of the angle by 12 and round to a buildable step.

1. Take the angle, for example 30 degrees.
2. tan(30°) = 0.5774.
3. 0.5774 × 12 = 6.93, so 30 degrees is a 6.93:12 roof.
4. Round to 7:12 (30.26°) for framing — a difference of a quarter degree, well inside cutting tolerance.

Common architectural angles map to these pitches: 15° ≈ 3.2:12, 20° ≈ 4.4:12, 22.5° ≈ 5:12, 25° ≈ 5.6:12, 30° ≈ 6.9:12, 35° ≈ 8.4:12, 40° ≈ 10.1:12 and 45° = 12:12 exactly. If a drawing calls for a round metric angle, expect a pitch that does not land on a whole step and check that the truss supplier can build it.

Where the degree value is the one that matters

• Mitre and bevel settings. A compound mitre saw is set in degrees, so a rafter plumb cut on a 6:12 roof is 26.57° from square — in practice 26.5°.
• Solar array design. Tilt angle, inter-row shading and irradiance models all work in degrees and never in X:12.
• Snow and wind load. ASCE 7 slope factors are tabulated against degrees, and the shedding thresholds around 30° and 70° are degree-based.
• European and Australian specifications. Tile and metal manufacturers publish minimum pitches in degrees, typically 12.5°, 15°, 17.5° and 22.5°.
• Photographic and drone survey output, which reports plane inclination in degrees before any conversion.

Framing, by contrast, stays in X:12 because a framing square, a speed square and a rafter table all work in rise per foot. The practical workflow is to measure or specify in whichever notation the trade uses, convert once, and record both numbers on the drawing so nobody re-derives them under pressure.

Two worked conversions

Example one — pitch to degrees. A garage roof measures 4.5 inches of rise over 12 inches of run. angle = arctan(4.5 ÷ 12) = arctan(0.375) = 20.56 degrees. Slope grade = 37.5 percent. Multiplier = √(4.5² + 12²) ÷ 12 = 12.816 ÷ 12 = 1.068, so a 24 × 22 foot footprint of 528 square feet carries 564 square feet of roof.

Example two — degrees to pitch. A European tile manufacturer specifies a minimum 17.5 degree pitch. tan(17.5°) = 0.3153, × 12 = 3.78. The nearest safe framing step is 4:12 (18.43°), because rounding down to 3.5:12 would put the roof under the manufacturer's limit and void the warranty. Always round up when a minimum is involved and down when a maximum is.

Degrees, metric ratios and percent in international practice

Outside North America the X:12 convention is unknown, and the same roof is described in one of three other ways. In the UK and Ireland pitch is quoted in degrees, and tile manufacturers publish a minimum pitch — 22.5 degrees for many interlocking concrete tiles, 30 degrees for plain clay tiles, 20 degrees for most fibre cement slates. In Australia and New Zealand degrees dominate too, with 12.5 degrees a common Colorbond metal minimum and 15 to 22 degrees typical on housing.

Continental Europe often uses a ratio in consistent units — 1:2 or 1:3 — which is rise over run in the same unit rather than rise per 12. A 1:2 roof rises one metre for every two metres of run, which is 26.57 degrees, exactly the same slope as 6:12. To convert a metric ratio to American pitch, divide the first number by the second and multiply by twelve: 1 ÷ 2 × 12 = 6:12. A 1:3 roof is 4:12 and 18.43 degrees; a 1:1 roof is 12:12 and 45 degrees.

Civil engineering, drainage design and highway work stay in percent grade because the numbers are small and add cleanly over long distances. Plumbing codes are a hybrid: the IPC specifies gutter and horizontal drain falls in inches per foot, which is the X:12 system with the twelve left implicit — a fall of 1/8 inch per foot is 1/8:12, or 0.6 degrees.

When you receive a specification in an unfamiliar notation, convert once, write all three values on the drawing, and state which one governs. Most cross-border errors happen when a 25 degree specification is read as a 25 percent grade — a difference of more than eleven degrees, and two full pitch steps in framing terms.

Frequently asked questions