Roof Pitch Calculator

How to use this calculator

Enter any two independent measurements. On site, roofers usually measure the rise over a 12-inch level: put 12 in in the run field, measure the vertical distance and enter it as the rise to read the pitch. From plans, enter the pitch and the run (half the span for a symmetric gable) to get the rise and rafter length. An angle from a digital level works as an input as well.

The rafter length shown is the sloped distance from the outside of the wall plate to the ridge centerline; add the overhang and subtract half the ridge board thickness for the cut length. Pitch is expressed as inches of rise per 12 inches of run, the convention used in US building codes.

The formula

pitch = 12 × rise / run

θ = arctan(rise / run)

rafter = √(rise² + run²)

rise: rise
run: run
x/12: pitch (inches of rise per 12 in of run)
θ: roof angle
slope: slope as percent
r: rafter length (sloped length)

Worked example

A gable roof rises 6 ft over a horizontal run of 12 ft (half the building width).

Pitch = 12 × rise / run = 12 × 6 / 12 = 6/12.
Angle = arctan(6/12) = 26.57°; slope = 50%.
Rafter length = √(6² + 12²) = 13.42 ft (before overhang).

A 6/12 roof sits at about 26.6°, and each rafter spans 13.42 ft from wall plate to ridge.

Common pitches

Pitch	Angle	Typical use
2/12	9.5°	Low-slope minimum for some shingles (with underlayment)
4/12	18.4°	Common ranch roofs; standard shingle minimum
6/12	26.6°	Very common residential pitch
8/12	33.7°	Steeper suburban roofs
12/12	45°	A-frames, Cape Cod style

Assumptions and limits

Measurements are horizontal run and vertical rise; the roof plane is flat.
Rafter length is a geometric line length; real cut lengths depend on overhang, ridge board and birdsmouth details.

Frequently asked questions

What does 4/12 pitch mean?

The roof rises 4 inches for every 12 inches of horizontal run, an angle of about 18.4° or a 33% slope.

What is the minimum pitch for asphalt shingles?

The International Residential Code requires at least 2/12, with double underlayment for slopes between 2/12 and 4/12.

How do I find pitch from the angle?

Pitch = 12 × tan(angle). Enter the angle here and the pitch fills in.