What is the formula to convert roof pitch to degrees?

Angle (degrees) = arctan(rise ÷ run). For the North American x-in-12 notation, that simplifies to arctan(x ÷ 12) — so a 6/12 pitch is arctan(6 ÷ 12) = arctan(0.5) = 26.57°.

How do I convert roof pitch to a percentage grade?

Grade (%) = (rise ÷ run) × 100. A 6/12 pitch is rise ÷ run = 0.5, so a 50% grade. A 4/12 pitch is 4 ÷ 12 = 0.333, so a 33.3% grade.

Is a 12/12 roof pitch 45 degrees?

Yes. At 12/12 the rise equals the run, so rise ÷ run = 1, and arctan(1) = 45°.

What's the difference between roof pitch and roof slope percentage?

Pitch is a ratio (rise/run, or x-in-12); slope percentage is that same ratio expressed out of 100 instead of out of 12 or 1. Degrees is the actual angle. All three describe the same steepness — pick whichever your drawings, saw or council form asks for.

Where do I measure rise and run to get my roof's pitch?

From the top of the wall plate to the underside of the ridge for the rise, and horizontally from the wall plate to the point directly below the ridge for the run. Our full measuring guide walks through doing this from the attic or the roof surface — see the link below.

In this section

Roof Pitch to Angle: Convert Rise/Run to Degrees & Grade

The formula, quick, plus a conversion table for common roof pitches — rise over run to degrees, and to percentage grade.

The formula

Angle (°) = arctan(rise ÷ run). That is the whole job. Roof pitch is a ratio: rise over run. Take the arctan of that ratio and you have the angle in degrees.

Want it as a grade instead? Same triangle: Grade (%) = (rise ÷ run) × 100.

1 rise. 2 run. 3 rafter (slope distance). 4 right angle where the run meets the rise. 5 pitch angle: the value both formulas above solve for.

Work it out by hand

Say you measure up in the roof space. Over a 3.6 m run, the rafter rises 1.8 m.

Divide rise by run. 1.8 ÷ 3.6 = 0.5.
Take the arctan for degrees. arctan(0.5) = 26.57°.
Or ×100 for grade. 0.5 × 100 = 50% grade.

That 0.5 ratio is also a 6/12 pitch. That is the x-in-12 style roofing suppliers and truss quotes use. It means 6 inches of rise for every 12 of run. Any unit works, as long as rise and run use the same one.

Common pitches, converted

Pitch (rise/run)	Angle	Grade
3/12	14.04°	25%
4/12	18.43°	33.3%
6/12	26.57°	50%
9/12	36.87°	75%
12/12	45.00°	100%

Do it in 5 seconds

Full guide: How to Work Out Pitch of Roof in Degrees. How to measure rise and run from the attic or the roof, the tools to use, and the minimum pitch each roofing material needs.
Next step: Rafter Length Calculation. Once you have the angle, work out how long to cut the rafters.
AU code minimum: Minimum Roof Pitch (NCC 2025).

Sources

Ramsey & Sleeper, Architectural Graphic Standards — roof pitch/angle reference tables.
Engineering ToolBox, “Roof Pitch — Convert to Angle” — reference conversion tables, cross-checked against the trig above.

Frequently asked questions

What is the formula to convert roof pitch to degrees?: Angle (degrees) = arctan(rise ÷ run). For the North American x-in-12 notation, that simplifies to arctan(x ÷ 12) — so a 6/12 pitch is arctan(6 ÷ 12) = arctan(0.5) = 26.57°.
How do I convert roof pitch to a percentage grade?: Grade (%) = (rise ÷ run) × 100. A 6/12 pitch is rise ÷ run = 0.5, so a 50% grade. A 4/12 pitch is 4 ÷ 12 = 0.333, so a 33.3% grade.
Is a 12/12 roof pitch 45 degrees?: Yes. At 12/12 the rise equals the run, so rise ÷ run = 1, and arctan(1) = 45°.
What's the difference between roof pitch and roof slope percentage?: Pitch is a ratio (rise/run, or x-in-12); slope percentage is that same ratio expressed out of 100 instead of out of 12 or 1. Degrees is the actual angle. All three describe the same steepness — pick whichever your drawings, saw or council form asks for.
Where do I measure rise and run to get my roof's pitch?: From the top of the wall plate to the underside of the ridge for the rise, and horizontally from the wall plate to the point directly below the ridge for the run. Our full measuring guide walks through doing this from the attic or the roof surface — see the link below.