FramersMath

FramersMath › Roof Pitch

Roof Pitch Calculator

Convert a roof pitch to degrees and percent slope, or work back from rise and run or an angle. You also get the rafter length per foot of run for commons and hips.

Pitch & angles

Enter any one
6 or 6/12
Angle (plumb cut)—
Pitch—
Percent slope—
Seat (level) angle—
Common rafter per ft of run—
Hip / valley per ft of run—

Pitch chart — angle and rafter length per foot of level run.

PitchAngleCommon / ftHip-val / ft

⚠ Check all math and verify with a licensed engineer and your local building department before cutting or building. Results are estimates.

What roof pitch means

Roof pitch is the number of inches a roof rises for every 12 inches it runs horizontally. A 6/12 roof (said "six in twelve") climbs 6" for every foot of run. Builders in the U.S. use pitch rather than degrees because it maps directly onto a framing square: 12 on the blade, the rise on the tongue.

RUN = 12" RISE = 6" 26.57° 13.42" PER FOOT OF RUN
A 6/12 pitch: 6" of rise per 12" of run is 26.57°, and the rafter is 13.42" long for every foot of run.

Converting pitch to degrees

The angle is the arctangent of rise over run: angle = atan(pitch ÷ 12). For 6/12 that's atan(0.5) = 26.57°. Going the other way, pitch = 12 × tan(angle), so a 30° roof is 6.93/12, just shy of 7/12.

Percent slope is rise over run × 100, so 6/12 is 50%. You'll see it on low-slope roofing specs and drainage plans.

Finding pitch from a measurement

On an existing roof, hold a level horizontally against the rafter or roof surface, mark 12" along it, and measure straight down (or up) to the roof. That measurement is your pitch. From the ground or attic you can also measure total rise and total run and enter them both. The calculator scales them to "x in 12".

Using the rafter factors

The common per ft column is the rafter length for each foot of run. Multiply it by the run in feet to get a rough rafter length, or use the rafter calculator to include the ridge and overhang. The hip-val per ft column does the same for hip and valley rafters, per foot of common run. Both match the tables stamped on a framing square.

Common pitches

FAQ

How do I convert roof pitch to degrees?

Divide the pitch by 12 and take the arctangent: angle = atan(pitch ÷ 12). A 4/12 roof is 18.43°, 6/12 is 26.57°, 8/12 is 33.69°, and 12/12 is 45°.

What is a 6/12 pitch in degrees?

A 6/12 pitch is 26.57°. It rises 6 inches for every 12 inches of horizontal run, a 50% slope.

How do I measure the pitch of an existing roof?

Place a level horizontally against the roof or the underside of a rafter, mark 12 inches along the level, and measure vertically from that mark to the roof. That number over 12 is the pitch.

What is the minimum pitch for asphalt shingles?

Most manufacturers allow 2/12 as an absolute minimum with a double underlayment, and 4/12 and up for a standard installation. Below 2/12, use a low-slope membrane. Check the shingle maker's instructions.

What is the difference between pitch and slope?

In everyday framing they mean the same thing: rise per 12 of run, like 6/12. Strictly speaking, old texts define pitch as rise over the full span (so a 6/12 slope is a ¼ pitch). This calculator uses the modern rise-in-12 convention.

Disclaimer: Results are estimates for planning and layout only. Check all math yourself and verify with a licensed engineer and your local building department before cutting or building. FramersMath is not a substitute for engineered plans, span tables or code review. See the full disclaimer.