Roof Pitch Calculator — angle, rafter, and slope

How it works

Roof pitch measures steepness as a ratio of vertical rise to horizontal run, and by convention the run is fixed at 12. So a roof that climbs 6 units for every 12 across is a 6:12 pitch. From any rise and run:

pitch = 12 × (rise ÷ run)

The same steepness as an angle is the arctangent of the rise over the run, and as a percent it is 100 × rise ÷ run. The rafter — the sloped board from the wall to the ridge — spans the rise and run as a right triangle, so its length is the hypotenuse:

rafter = √(rise² + run²)

Note the run here is the horizontal distance the rafter covers, which for a simple gable is half the building's span (wall to ridge), not the whole width.

Worked example

For a 6 in rise over a 12 in run, the pitch is 12 × (6 ÷ 12) = 6, i.e. a 6:12 roof. The slope angle is arctan(6 ÷ 12) = arctan(0.5) = 26.6°, the slope percent is 100 × 6 ÷ 12 = 50%, and the rafter length is √(6² + 12²) = √180 = 13.42 in for each 12 in of run.

Frequently asked questions

What is roof pitch?

Roof pitch is the steepness of a roof, expressed as the vertical rise per 12 units of horizontal run — for example 6:12 means 6 inches of rise for every 12 inches of run. A higher first number means a steeper roof.

What does a 6:12 pitch mean?

It means the roof rises 6 inches for every 12 inches you move horizontally. That works out to a slope angle of about 26.6° and a 50% slope — a common, moderate residential pitch that sheds water and snow well while staying walkable.

How do I find the roof angle from the pitch?

Take the arctangent of the rise divided by the run. A 6:12 pitch is arctan(6 ÷ 12) ≈ 26.6°; a 12:12 pitch is arctan(12 ÷ 12) = 45°; a 4:12 is about 18.4°.

How long should the rafter be?

The rafter spans the rise and run as a right triangle, so its length is √(rise² + run²). For a 6:12 pitch that is √(6² + 12²) = 13.42 in per 12 in of run; multiply by the number of feet of run and add for the overhang.

What counts as a low or steep pitch?

Pitches below 4:12 are considered low-slope and often need special membranes; 4:12 to 9:12 is the common walkable range; and anything above about 9:12 is steep, usually requiring roof jacks or staging to work on.

How do I measure my roof's pitch?

Hold a level horizontally against the roof, measure 12 inches along it, and measure straight down from the 12-inch mark to the roof surface — that vertical distance is the rise in a 12-inch run, i.e. the "rise" number of the pitch.