What is roof pitch in X-in-12 terms?

Pitch is the vertical rise for every 12 units of horizontal run. A 6-in-12 pitch rises 6 inches for each 12 inches across. The angle equals the arctangent of rise divided by 12, so 6-in-12 is about 26.57 degrees.

How is the common rafter length found?

The horizontal run is half the building width. The rafter is the hypotenuse: run times the square root of (1 plus (rise/12) squared), plus the sloped length of the overhang. This is the line length along the top of the rafter.

How is ridge height calculated?

Ridge height above the wall plate equals the run times the pitch ratio: half the width times rise divided by 12. A 24 ft wide building at 6-in-12 has a run of 12 ft and a ridge 6 ft above the plate.

Why is the hip rafter longer than the common rafter?

A hip rafter runs diagonally across the corner, so its horizontal run is the diagonal of the two adjacent runs. The tool uses a 17-per-12 unit run rather than 12, giving the longer length that meets the ridge at the corner.

How many rafters do I need?

Divide the building length by the spacing on centre, round up, and add one for the closing rafter at the far end. The count is per roof side; a gable roof needs that many on each slope plus the two end pairs.

Roof Pitch & Rafter Length Calculator

Framing a roof starts with two numbers: how far each rafter must reach and at what angle. This calculator turns a building width and roof pitch into the common rafter length with overhang, the ridge height, the hip rafter length, and the rafter count, so you can cut and order with confidence.

How it works

Pitch is a rise over a 12-unit run. From half the building width (the run) the geometry follows:

angle      = arctan(rise / 12)
common len = run × √(1 + (rise/12)²) + overhang × √(1 + (rise/12)²)
ridge ht   = run × (rise / 12)
hip len    = run × √(1 + (rise/12)² + 1)     (diagonal run uses 17-per-12)
count      = ceil(length / spacing) + 1

The factor under the square root for the hip adds a second horizontal component because the hip travels diagonally across the plan corner.

Example and notes

A 24 ft wide building at 6-in-12 has a 12 ft run. The common rafter line length is 12 x sqrt(1 + 0.25) = 13.4 ft, plus the sloped overhang. The ridge sits 6 ft above the plate (26.57 degrees). The hip rafter is 12 x sqrt(2.25) = about 18 ft. Add the ridge board thickness deduction at the peak when cutting, and remember these are line lengths measured along the rafter top edge.