Roof pitch calculator x/12, degrees and percent

The formulas

Every result comes from the rise per 12 units of run. Convert your reading to x/12 first, then everything else follows.

Pitch from rise and run

pitch = rise ÷ run × 12 Gives the rise per 12 of run, written x/12.

Pitch from an angle

pitch = tan(angle) × 12 Use the angle in degrees from a digital level or phone app.

Pitch from a percent

pitch = percent ÷ 100 × 12 A 25% slope rises 25 for every 100 of run.

Angle

angle = atan(rise ÷ 12) In degrees, rounded to 0.1.

Percent

percent = rise ÷ 12 × 100 Rounded to 0.1.

Pitch factor

√(1 + (rise ÷ 12)²) Sloped length per foot of horizontal run. Multiply plan area by it to get true area.

Hip / valley factor

√(2 + (rise ÷ 12)²) Hip or valley length per foot of common run, when both roof planes have the same pitch.

Rafter length

rafter = horizontal run × pitch factor Measured along the slope, before any ridge or plumb-cut adjustments.

Worked example: one reading from each mode

Three readings you might get on a real job: a tape and level on the roof, a phone app on a rafter, and a slope printed on a drawing.

1. Rise and run: the level reads 7.5 in of rise over 12 in of run. Pitch = 7.5 ÷ 12 × 12 = 7.5/12.
2. Angle = atan(7.5 ÷ 12) = atan(0.625) = 32.0°. Percent = 7.5 ÷ 12 × 100 = 62.5%.
3. Pitch factor = √(1 + 0.625²) = √(1 + 0.390625) = √1.390625 = 1.179. Hip/valley factor = √(2 + 0.390625) = √2.390625 = 1.546.
4. Rafter for a 14 ft horizontal run: 14 × 1.179 = 16.5 ft.
5. Angle: a phone app on a rafter reads 33°. Rise = tan(33°) × 12 = 0.6494 × 12 = 7.8, so the pitch is 7.8/12 (just under 8/12). Percent = 0.6494 × 100 = 64.9%. Pitch factor = √(1 + 0.6494²) = √1.4217 = 1.192.
6. Percent: a drawing shows a 25% slope. Rise = 25 ÷ 100 × 12 = 3, so the pitch is 3/12. Angle = atan(3 ÷ 12) = atan(0.25) = 14.0°. Pitch factor = √(1 + 0.25²) = √1.0625 = 1.031.

7.5/12 = 32.0° = 62.5% with a 1.179 pitch factor and a 16.5 ft rafter over 14 ft of run; 33° ≈ 7.8/12 (factor 1.192); 25% = 3/12 = 14.0° (factor 1.031).

Roof pitch chart: 2/12 to 14/12

Rise over run, and why roofers write x/12

Pitch is how many inches a roof climbs for every 12 inches it travels horizontally. A 6/12 roof rises 6 in per foot of run; a 12/12 roof rises a foot per foot, which is 45°.

You don't have to measure over exactly 12. Measure any rise and run in the same unit, divide the rise by the run and multiply by 12. A rise of 10 in over a run of 24 in is 10 ÷ 24 × 12 = 5/12. Odd readings like 7.5/12 are normal on older houses and additions; round only when you order materials.

Converting degrees and percent

Phone apps and digital levels give an angle. Engineers' and architects' drawings often give a percent slope. Both convert to the same x/12 number: the tangent of the angle times 12, or the percent divided by 100 and times 12.

Don't mix them up. A 45° roof is 12/12, which is also 100%. A 45% slope is only 5.4/12, about 24°. If a drawing number looks too steep or too flat for the house in front of you, check which one it is.

Measuring pitch on site with a level and tape

Mark 12 in on a 2 ft level. Set one end on the roof surface (or on the underside of a rafter in the attic), hold the level dead level, and measure straight down from the 12 in mark to the roof. That measurement is the rise: 7.5 in means 7.5/12.

Take the reading on a clean, flat spot, not on a lifted shingle, a ridge cap or a sagging section, and repeat it on each roof plane you can reach. Additions, porches and dormers often have their own pitch. If you can't safely get up, read it from the street with the Street View tool above or trace the roof from satellite imagery.

Pitch factor, and why it matters for squares

A roof's footprint is smaller than the surface you actually cover. The pitch factor turns plan (flat) measurements into true sloped measurements: multiply the plan area by the factor to get the true area, then divide by 100 for squares.

At 4/12 the difference is about 5%; at 12/12 it is about 41%. A 2,000 sq ft footprint at 8/12 is 2,000 × 1.202 = 2,404 sq ft, or 24.04 squares before waste. Order off the plan area and you come up short on every steep job.

Hips and valleys run diagonally, so they use the larger hip/valley factor. Rakes use the pitch factor, while eaves and ridges are level and need no factor at all.

When the roof has several planes and pitches, measuring each one by hand gets slow. RoofStruct offers free, unlimited self-serve measuring and PDF reports, no card: trace the facets on satellite imagery, set each pitch, and the true areas and edge lengths are worked out for you.

Roof pitch questions

How do I calculate roof pitch?

Measure the rise and run in the same unit, divide the rise by the run and multiply by 12. The result is the pitch in x/12, for example 10 in of rise over 24 in of run is 5/12.

How do I convert a roof angle in degrees to pitch?

Take the tangent of the angle and multiply by 12. A 30° roof is tan(30°) × 12 = 6.9/12, just under 7/12.

What is a pitch factor?

It is the sloped length per foot of horizontal run, √(1 + (rise ÷ 12)²). Multiply the plan (footprint) area by it to get the true roof area; a 6/12 roof has a factor of 1.118.

What pitch counts as a low-slope roof?

In general trade use, roofs below about 4/12 are treated as low-slope and often need extra underlayment or a different roofing system. Your local code and the manufacturer's instructions set the actual limits.

Is a 45% slope the same as a 45° roof?

No. A 45° roof is 12/12, which is a 100% slope. A 45% slope is 5.4/12, about 24.2°.