Formula
Area is the footprint times the rafter multiplier, √(1 + (pitch ÷ 12)²). One square is 100 square feet. Waste is a percent on the area and on the linear goods. Bundles are the order squares times bundles per square, rounded up. Underlayment rolls, drip-edge sticks, ridge bundles, and starter bundles all round up.
area = length × width × √(1 + (pitch / 12)²)
squares = area ÷ 100
gable eaves = 2 × length, rakes = 2 × width × multiplier, ridge = length
hip eaves = 2 × (length + width), ridge = |length − width|
each hip = (shorter side ÷ 2) × √(2 + slope²), and there are four
A uniform pitch covers the same area on a hip as on a gable. The hip only changes the lines. Three bundles per square fits 3-tab and many architectural bundles. The bundle in your hand may differ, so the count is editable. Fifteen-pound felt is often sold as 400 square feet a roll. Synthetic is often near 1,000. Hip-and-ridge cap is often 25 to 33 linear feet a bundle. Starter is often near 100. Those coverage numbers are package figures, not a standard, and the fields are there so you can replace them. Nails are about 320 per square with four nails, or 480 with six, which is a note rather than an order quantity. The pitch calculator and the rafter calculator use this same multiplier. The truss calculator turns it into king-post, Fink, or Howe board lengths, and it does not size the truss.
Worked examples
40 × 30 ft, 6/12, gable, no thinking about waste yet. Area is 1,341.6 ft², 13.42 squares. Eaves are 80 ft, rakes are 67.1 ft, ridge is 40 ft.
The same roof with 10% waste and 3 bundles per square. Order squares are 14.76. Bundles round up to 45. Underlayment at 400 ft² a roll rounds up from the wasted area. Drip edge is the eaves plus the rakes, plus waste, in 10 ft sticks.
The same footprint as a hip at 6/12. Area does not change. Ridge drops to 10 ft. Four hips are added. Bump the waste toward 15% if the cuts justify it.
Reference
Pitch multipliers, shared with the pitch calculator.
| Pitch | Multiplier |
|---|---|
| 4/12 | 1.0541 |
| 5/12 | 1.0833 |
| 6/12 | 1.118 |
| 7/12 | 1.1577 |
| 8/12 | 1.2019 |
| 9/12 | 1.25 |
| 12/12 | 1.4142 |
Questions
How many squares is a 40 by 30 foot roof at 6/12?
The footprint is 1,200 ft². A 6/12 multiplies by 1.118, so the roof is 1,342 ft², or 13.42 squares. At 10% waste and 3 bundles per square, order 45 bundles.
Does a hip roof use the same area?
Yes, when every plane is the same pitch. Area is footprint times the multiplier either way. The hip shortens the ridge and adds four hip lines. Ridge length is the difference of the two footprint sides. Each hip is (shorter side ÷ 2) × √(2 + slope²).
How much waste should I add?
10% is a common gable allowance and 15% a common hip allowance. Valleys, dormers, and a cut-up plan need more. The field is yours. Bundles round up after the waste is applied.
Sources
- The multiplier is the hypotenuse of a unit run and the slope, the same function as the roof pitch calculator. A 6/12 is √1.25 = 1.11803.
- One roofing square = 100 ft². Bundle count defaults to 3 per square and is editable.
- Underlayment default 400 ft² per roll is a 15-lb felt package figure. Synthetic rolls are often near 1,000 ft². Hip-and-ridge default 25 linear feet and starter default 100 linear feet are package figures, often 25–33 for cap, and they are not a standard.
- Siding calculator for wall squares. A roofing square and a siding square are both 100 square feet, of different materials.