Rafter Length and Roof Pitch Calculator

A common rafter is the hypotenuse of a right triangle whose legs are the run (level distance) and the rise (vertical height), so its length is √run² + rise². On a 6/12 roof with a 12 ft run, the rise is 6 ft and the rafter is √144 + 36 = √180 ≈ 13.42 ft before you add the overhang.

How to use the rafter calculator

1. Enter the run. For a gable roof this is half the span (the building's width from outside of wall to outside of wall). A 24 ft wide house has a 12 ft run.
2. Choose how you know the slope: as a pitch such as 6 (meaning 6 in 12), as the total rise from the top of the wall to the ridge line, or as an angle in degrees. Switching modes converts the current slope for you.
3. Enter the overhang as a level distance, or 0 for none. The calculator turns it into the extra length along the rafter.
4. Read the results: the total line length, also in feet, inches and sixteenths, plus the pitch, angle, rise, grade and slope factor, and every step of the arithmetic.

Roof pitch explained

In the US and Canada, roof slope is written as inches of rise per 12 inches of run. A 6/12 roof (say "six in twelve") climbs 6 in for every 12 in it runs horizontally. Since a pitch is just the two legs of a small right triangle, the same triangle, together with the Pythagorean theorem formula, gives every other way of describing the slope:

The slope factor is the hypotenuse of that small triangle divided by 12: the length of rafter for each unit of run. Multiply any run by it to get the length along the slope. For 6/12 it is √36 + 144 ÷ 12 = √180 ÷ 12 ≈ 1.118, so every foot of run needs about 1.118 ft (13.42 in) of rafter.

A note on words: strictly, pitch is the rise divided by the whole span, so a 6/12 slope is a "1/4 pitch", while slope is rise over run. In everyday use, "6/12 pitch" and "6-in-12 slope" mean the same thing, and that is how the calculator uses the word.

Roof pitch table

Two rows come out as whole numbers. A 5/12 roof gives exactly 13 in of rafter per foot of run and a 9/12 roof exactly 15 in, because 5-12-13 and 9-12-15 are Pythagorean triples (the second is the 3-4-5 triangle scaled by 3). A 12/12 roof is a 45° slope, a 45-45-90 triangle, so its slope factor is √2.

Worked examples

From line length to the cut board

The calculator gives the theoretical line length: the hypotenuse from the center of the ridge to the outside of the wall, plus the tail. Turning that into a cut rafter involves a few adjustments that depend on your materials and plans, so treat the following as an outline rather than a framing manual:

• Ridge board. The run is measured to the center of the ridge, but the rafter stops at the ridge board's face. Shorten it by half the ridge thickness measured level, times the slope factor along the rafter. For a 1½ in ridge board on a 6/12 roof that is 0.75 × 1.118 ≈ 0.84 in.
• Birdsmouth. Where the rafter crosses the wall, a notch with a level seat cut and a vertical heel cut lets it sit flat on the top plate. The depth of that notch decides where on the board the line length is laid out.
• Plumb cuts and tail. The ridge end and usually the tail end are cut vertical (plumb) at the roof angle, so the board must be a little longer than the line length. Lumber comes in 2 ft steps, so a 14.53 ft line length usually means a 16 ft board.

Rafter sizes, spacing and allowable spans are a structural question that this math does not answer; they come from span tables and the building code that applies to your project. Hip and valley rafters cross the plan diagonally, so they need the theorem twice, the same idea as the Pythagorean theorem in 3D. For squaring the walls the rafters sit on, see the Pythagorean theorem in construction, and for the trades that use this math daily, jobs that use the Pythagorean theorem.