Roof pitch and roofing squares explained

Every roofing quote rests on one number: how many squares of roof there are. Shingles, underlayment, labor, disposal and waste are all worked out from it. If that number is wrong, everything priced from it is wrong too, so it helps to know where it comes from.

The arithmetic takes a calculator and a few minutes. Measuring the inputs accurately is harder, and that part belongs to trained professionals on the roof or to good imagery.

What a square is

A roofing square is 100 square feet of roof surface. A roof with 2,400 square feet of surface is 24 squares. Roofers use squares because materials are sold that way. Most common asphalt shingles are packed so that three bundles cover a square, though some heavier styles take four or more.

Square feet of roof is not the same as square feet of house. A one-story house with 1,600 square feet of floor can easily have 20 squares of roof once the overhangs and the slope are included.

What pitch means

Pitch describes how steep a roof is. In the United States it is written as rise over run: how many inches the roof climbs for every 12 inches it runs horizontally. A 4/12 roof rises four inches per foot and is fairly shallow. A 12/12 roof rises a foot for every foot across, which is a 45-degree slope.

Pitch matters for two reasons. Steeper roofs have more surface over the same footprint, so they need more material. They are also slower and more hazardous to work on, which is why many contractors charge more per square once a roof passes roughly 7/12 or 8/12.

From footprint to surface area

Measured from above, from a plan or from imagery, a roof section has a footprint. To turn that footprint into surface area, multiply it by a pitch factor. The factor is the length along the slope divided by the horizontal distance it covers. To work it out for a pitch of rise over 12, divide the rise by 12, square that, add one, and take the square root. For 6/12, 6 divided by 12 is 0.5, 0.5 squared is 0.25, adding one gives 1.25, and the square root of 1.25 is 1.118.

Factors for common pitches, rounded to three decimal places:

• 3/12: 1.031
• 4/12: 1.054
• 5/12: 1.083
• 6/12: 1.118
• 7/12: 1.158
• 8/12: 1.202
• 9/12: 1.250
• 10/12: 1.302
• 12/12: 1.414

Say a plane has a footprint of 600 square feet at 8/12. Its surface area is 600 multiplied by 1.202, or 721 square feet. The same footprint at 4/12 would be 632 square feet. That gap of nearly a full square comes from one plane, and across a whole roof it adds up quickly.

Why each plane gets its own pitch

Many houses do not have a single pitch. A main roof at 8/12 may sit above a porch at 4/12 and a dormer at 10/12. Additions built decades apart often differ slightly even when they look alike from the street. Applying one pitch to the whole footprint can put a total off by several percent, so careful measurements treat each plane separately and then add them up.

Recalculating that total a second way, from the same footprint and the same pitch readings, is not an independent check, because a misread pitch carries into both answers. A real cross-check compares totals that do not share inputs, such as an on-site measurement and an aerial report for the same roof. How roofs are measured covers this in more detail.

Waste

No roof uses only its surface area in shingles. Shingles are cut at hips, valleys and rakes and around penetrations, and the offcuts are thrown away. A waste allowance added to the measured area covers those cuts.

A simple gable roof is often figured at about 10 percent. A roof with many hips and valleys might need 15 percent or more. Many measurement reports show totals at several percentages so the estimator can choose. On a homeowner's quote you should be able to find the waste figure, even if it has been folded into the square count.

Starter strip and ridge cap are counted separately

Starter strip and ridge cap are not part of the waste percentage. They are separate products ordered by the linear foot. Starter strip runs along the eaves, and often the rakes, so its quantity comes from the eave and rake lengths. Ridge cap covers ridges and hips, so its quantity comes from those lengths. Drip edge is figured the same way, from the eave and rake lengths.

A worked example

Take a one-story house with a simple gable roof. Including the overhangs, the footprint is 50 feet by 34 feet, or 1,700 square feet. The ridge runs the 50-foot length, and the pitch is 6/12 on both sides.

1. Surface area: 1,700 multiplied by 1.118 is 1,901 square feet.
2. Squares: 1,901 divided by 100 is 19.0 squares.
3. With 10 percent waste: 20.9 squares, which most suppliers would round up to 21.
4. Rake length: each side runs 17 feet horizontally, and 17 multiplied by 1.118 is 19.0 feet along the slope. Four rakes total 76 feet.
5. Starter strip: 100 feet of eave, plus 76 feet of rake if starter is used there too, for 176 linear feet.
6. Ridge cap: one ridge of 50 feet.

If a quote for this roof listed 25 squares, that would be worth asking about. It might include a detached garage or a more generous waste allowance, or it might be a rough estimate nobody checked.

Where pitch shows up on a diagram

On most diagrams the pitch is written inside each plane, next to its label and its area, and a totals table adds the planes together. To see how one plane contributes, take its footprint from the drawing, multiply by the factor for its pitch, and you should land within a few square feet of the area written on it. How to read a roof diagram explains the layout.

A note on safety

Never climb onto your roof with a tape measure to check a quote, even on a low, one-story house. For a rough sense of scale, pace out the wall lengths at ground level.