Roof Pitch Calculator

Enter the rise and run of your roof, or the angle in degrees, and get the pitch as an X:12 ratio, the angle, the pitch multiplier and the slope percentage. Results update as you type. No signup.

How the roof pitch calculator works

Roof pitch is a way of describing how steep a roof is. In the United States it is almost always written as a ratio of vertical rise to horizontal run, with the run fixed at 12 inches. A 6:12 roof rises 6 inches for every 12 inches it travels sideways. A 12:12 roof rises 12 inches for every 12 inches of run, which is a 45-degree slope. Everything this calculator produces comes from that one relationship between rise and run.

The variables

• Rise is the vertical distance the roof climbs. On an existing roof you measure it with a level and a tape: hold a 12-inch level flat against the roof surface with one end touching the shingles, then measure straight down from the raised end to the roof. That measurement is the rise per 12 inches of run.
• Run is the horizontal distance covered while the roof gains that rise. Run is not the same as the rafter length, which is the sloped distance along the roof surface. On a plan drawing, run is usually half the building width for a simple gable.
• Angle is the slope expressed in degrees from horizontal. Architects and engineers often work in degrees, while roofers and building codes work in X:12 pitch. Both describe the same roof.

You can enter rise and run in any units as long as they match. Inches are the convention, but 2 feet of rise over 4 feet of run gives exactly the same result as 6 inches over 12 inches because only the ratio matters.

Formula 1: pitch ratio (X:12)

The calculator scales whatever you entered to a 12-inch run:

X = 12 × rise ÷ run

If you measured 5 inches of rise over 10 inches of run, X = 12 × 5 ÷ 10 = 6, so the pitch is 6:12. The result is rounded to two decimal places. Real roofs are framed at whole or half-inch pitches, so a reading such as 5.9:12 almost certainly means a 6:12 roof with a slightly imprecise measurement.

Formula 2: angle in degrees

The angle comes from the inverse tangent (arctangent) of rise over run:

angle = atan(rise ÷ run)

For a 6:12 roof, atan(6 ÷ 12) = atan(0.5) = 26.57 degrees. The relationship is not linear. Going from 4:12 to 8:12 doubles the pitch number but only takes the angle from 18.4 to 33.7 degrees. A 24:12 roof is still only 63.4 degrees. In angle mode the calculator runs this in reverse: rise per 12 inches of run = 12 × tan(angle).

Formula 3: pitch multiplier

The pitch multiplier (also called the roof slope factor or area factor) converts the flat footprint of a roof into its true sloped surface area. It is the length of the sloped surface divided by the horizontal run, which comes straight from the Pythagorean theorem:

multiplier = √(rise² + run²) ÷ run

For 6:12, that is √(36 + 144) ÷ 12 = √180 ÷ 12 = 1.118. A house with a 1,500 square foot footprint under a 6:12 gable roof therefore has about 1,500 × 1.118 = 1,677 square feet of actual roof surface. The same number also gives rafter length: multiply the horizontal run of a rafter by the multiplier to get its sloped length before adding overhang. The multiplier is identical to 1 ÷ cos(angle), which is the form you will see in engineering references.

Formula 4: slope factor as a percentage

Slope as a percentage is simply rise divided by run, multiplied by 100:

slope % = rise ÷ run × 100

A 6:12 roof is a 50% slope and a 12:12 roof is a 100% slope. Percent grade is common in civil and drainage work and on some product data sheets. Note that some roofing suppliers use the phrase “slope factor” to mean the pitch multiplier above rather than the percentage. We show both on this page so you can match whichever convention your source uses.

What changes the number

Pitch itself is fixed by how the roof was framed, but the number you get from the calculator depends on how carefully you measure. Three things move it:

• Measuring over too short a distance. A 12-inch level is the minimum. Measuring rise over 24 or 48 inches of run and letting the calculator scale it to 12 halves or quarters your measurement error.
• Measuring on shingles instead of the deck. Shingle overlaps, ridge caps and curled tabs add a few degrees of local error. Measure mid-slope on a flat course, or from the underside of a rafter in the attic, which is usually the most accurate option.
• Mixing units. Rise in inches and run in feet will give a pitch twelve times too small. Keep both inputs in the same unit.

Why pitch matters for cost and materials

Pitch feeds almost every other roofing calculation. Steeper roofs have more surface area for the same footprint, which means more shingles, more underlayment and more labor. Contractors also add a steepness surcharge: most consider anything above 6:12 “non-walkable” and price it higher because of staging, harnesses and slower installation. Roofs at 12:12 and above can add 20 to 40 percent to labor. Pitch also determines which products are allowed. Asphalt shingles generally require at least 2:12, with extra underlayment between 2:12 and 4:12, while anything flatter needs a membrane or standing-seam metal system.

Once you have your pitch, use the roof area calculator to turn your footprint into true surface area, the roofing square calculator to convert that area into squares with a waste allowance, and the roof replacement cost guide to see what that square count is likely to cost in your area.

Roof pitch reference chart