Carpentry Math

Roof Pitch Calculator

Measure 12" level along the rafter, then straight up to it: that is the rise per 12.

Rafter length for a span

Turn rise and run, or an angle, into pitch, degrees and rafter factor.

How to use the roof pitch calculator

  1. Measure the vertical rise over a level run — 12" of run makes it simple.
  2. Or switch to Angle if you know the roof angle in degrees.
  3. Open Rafter length for a span to get the slope length over any horizontal run.

Roof pitch formulas

Pitch = rise ÷ run × 12 (written x/12)

Angle = arctan(pitch ÷ 12) · Slope % = pitch ÷ 12 × 100

Rafter factor = √(1 + (pitch ÷ 12)²)

Every pitch from 1/12 to 24/12, with its angle, rafter factor and suitable roofing, is in the roof pitch chart. To cut the rafters themselves, use the rafter calculator.

Frequently asked questions

How do I calculate roof pitch?

Measure the rise over a known horizontal run, then scale it to 12: pitch = rise ÷ run × 12. A roof that rises 30" over 60" of run is 30 ÷ 60 × 12 = 6, a 6/12 pitch.

How do I measure roof pitch without getting on the roof?

From the attic, hold a level against the underside of a rafter, mark 12" along the level, and measure straight up from that mark to the rafter. Or measure the gable end from the ground: the height of the peak above the wall top over half the building width.

How do I convert roof pitch to degrees?

Angle = arctan(rise ÷ 12). A 4/12 roof is 18.4°, 6/12 is 26.6°, 8/12 is 33.7°, 12/12 is 45°.

What is the most common roof pitch?

On US houses, between 4/12 and 9/12 — steep enough for asphalt shingles with standard underlayment, and still walkable. 6/12 is a typical middle value.

What is the minimum pitch for shingles?

The IRC allows asphalt shingles down to 2/12, but slopes from 2/12 to 4/12 need two layers of underlayment. Below 2/12 you need a low-slope membrane or metal rated for it.

What is the rafter factor?

The length of rafter per foot of horizontal run: √(1 + (pitch ÷ 12)²). Multiply the run by it to get the rafter length along the slope — 1.118 for a 6/12 roof.