Rafter Length From Rise, Run and Pitch (With Multiplier Table)

Any roof can be framed from three numbers: the run of horizontal distance the rafter covers, the rise in vertical height it gains, and the pitch that connects them. Get the length wrong and the rafter lands short of the ridge or overshoots the wall line. Get it right and the whole assembly squares up on the first try. This guide covers the geometry, the pitch-to-multiplier shortcut that framers use instead of trigonometry, and the two deductions that people most often forget.

The three numbers, defined once

Run is half the building width measured to the outside of the wall, adjusted for the overhang if you are cutting a full rafter. Rise is the vertical height from the top plate to the top of the ridge board. Pitch is the relationship between them, written as inches of rise per 12 inches of run — a 6/12 roof rises 6 inches for every foot of horizontal travel.

For a 24-foot-wide building with a 12-inch overhang on each side, the total horizontal span a rafter covers is 24 feet + 2 feet of overhang = 26 feet, so the working run is 13 feet. That 13-foot figure is what every subsequent calculation uses.

The pitch multiplier shortcut

Rather than solving a right triangle each time, framers use a multiplier per pitch and multiply it by the run. The multiplier is the hypotenuse divided by 12 in the classic 12-inch ratio.

Run × multiplier gives the rafter length along the top edge, measured from the outside of the wall to the ridge centerline — before deductions. Note how quickly the multiplier climbs: at 12/12 the same 13-foot run needs nearly 5 feet more material than at 3/12.

Worked example: a 6/12 gable

Take a 24-foot building with 12-inch overhangs and a 6/12 pitch. Run including overhang is 13 feet. Length along the top edge = 13 × 1.1180 = 14.53 feet, or 14 feet 6.4 inches. If the ridge board is a 2×8 (actually 1.5 inches thick), the rafter must be shortened by half the ridge thickness measured along the plumb line — roughly 0.75 inches of horizontal travel, or about 0.84 inches of rafter length at 6/12. Round to a working length of 14 feet 5½ inches, then deduct for the birdsmouth seat cut separately.

Add the overhang: if the building measurement already included the 12-inch overhang, that length is final. If it did not, add the overhang run × the same multiplier — 1 ft × 1.1180 = 1.12 feet, or about 13½ inches of rafter per side.

Two deductions people forget

• Ridge thickness: the rafter stops at the side of the ridge board, not at its center. Half the ridge thickness, measured horizontally, must come off the run before multiplying.
• Birdsmouth seat and heel: the seat cut and the plumb cut at the wall line remove material, and a seat cut deeper than one-third the rafter depth weakens the member. Keep the seat shallow and adjust the heel height rather than cutting deeper.

A third, less obvious one: when the ridge is not yet set, framers often cut the first rafter full-length and use it as a template, then measure the second from it. That is faster and avoids compounding rounding errors across the pair.

Common spans and the material they imply

For standard 2×10 rafters at 16 inches on center, a 6/12 roof comfortably spans about 15 feet of total span on many species and grades, meaning a 13-foot run is well within range. At 8/12 the same member is doing more work per foot of run and spans slightly less. For runs beyond about 16 feet, engineered lumber or a mid-span support becomes the practical answer, and the multiplier math stays the same — you just apply it to a shorter run per member.

A quick cross-check before ordering lumber: compute the per-rafter length, multiply by the number of rafters (twice the count per side, plus two for the end), and add 10 percent for waste and miscuts. For board-foot and volume checks, the volume calculator handles the prism math once you have the dimensions.

Checking the result on site

Before cutting a full set, cut one rafter and test-fit it against the ridge. The plumb cut at the ridge should meet the ridge face flush along its full width, and the heel should sit flat on the top plate with the seat cut fully bearing. If there is a gap at the ridge face, the deduction was too generous; if the rafter rides high over the ridge, the deduction was too small. Adjusting one template is cheap — adjusting fourteen rafters is not.

Measure the rise at the ridge rather than trusting the pitch label. A roof built to a nominal 6/12 that is actually 6.5/12 over a 13-foot run is nearly an inch longer per rafter, which is enough to throw off the ridge line on a long span. Verifying with a level and a tape at the ridge takes a minute and settles the question.

Frequently asked questions

Is the run half the building width? For a symmetric gable, yes — measured to the outside face of the wall, then adjusted for the ridge thickness and the overhang.

Can I use 2×6 rafters for a shed at 12/12? Often yes for short spans, but the steeper pitch increases the load along the member; check a span table for your species, grade, and snow load rather than assuming.

What is a common rafter versus a hip rafter? A common rafter runs perpendicular to the ridge and uses the multiplier above. A hip rafter runs diagonally and needs an additional factor of about 1.414 applied to the run before the pitch multiplier is used.

How much overhang is typical? 12 to 24 inches on gable ends, subject to local wind and snow requirements. The overhang adds length but does not add to the span the rafter has to support.