Rafter Length Converter

Roof pitch describes how steep a roof is. It is expressed as the number of inches of rise per 12 inches of horizontal run (e.g., 6/12 means 6 inches of rise for every 12 inches of run).

The fundamental rafter length formula: Rafter length uses the Pythagorean theorem:

• Rafter Length = sqrt(Run^2 + Rise^2)
• Per foot of run: Rafter Length per foot = sqrt(12^2 + Pitch^2) / 12

For example, with a 6/12 pitch:

• Rafter per foot = sqrt(144 + 36) / 12 = sqrt(180) / 12 = 13.416 / 12 = 1.118 feet per foot of run

Complete rafter length table per foot of run:

Calculating total rafter length: Total rafter = Rafter per foot x Total run (in feet) + Overhang

• The “run” is the horizontal distance from the outside wall to the ridge.
• Add the desired eave overhang (usually 12-24 inches / 30-60 cm). Note that the overhang is quoted level, so it lengthens along the slope by the same factor as the run does.
• Add 6-12 inches for the ridge cut and birdsmouth cut waste before you pick a board length.

The run is not simply half the building width. It is half the width minus half the thickness of the ridge board, because the run is measured to the centre of the ridge. A 24-foot building with a 1.5-inch ridge has a run of 12 feet less 0.75 inch, or 11.9375 feet. That is under an inch, and it is the single most common reason a first set of rafters sits proud at the peak. On a structural ridge beam of 3.5 or 5.5 inches the deduction is large enough that skipping it will not go unnoticed.

Example calculation: A building is 24 feet wide with a 6/12 pitch and 18-inch eave overhang.

• Run = 24/2 = 12 feet (before the ridge deduction)
• Rafter per foot = 1.118
• Rafter length = 12 x 1.118 = 13.42 feet
• Add overhang: 1.5 x 1.118 = 1.68 feet
• Total = 15.09 feet
• Add 8 inches of cut waste and you need 15.76 feet, so buy 16-foot stock

Lumber comes in even lengths, but not every even length. Yards stock 8, 10, 12, 14, 16, 20 and 24 foot boards. There is no 18 and no 22, so a calculation that rounds to the next even number will occasionally send you looking for a board that does not exist.

Pitch to degrees conversion:

• Degrees = arctan(pitch / 12) x (180 / pi)

Common roof pitch ranges:

• Low slope: 1/12 to 3/12 (requires special roofing materials)
• Standard slope: 4/12 to 9/12 (most residential roofs)
• Steep slope: 10/12 to 12/12 (dramatic appearance, more expensive)