How the roofing calculator works
Footprint, pitch, then materials. Roof area is the flat footprint area divided by the cosine of the pitch angle — a 1,500 sq ft footprint at a 30 degree pitch is 1,732.05 sq ft of roof. The pitch angle comes from the rise and run: a 6/12 pitch (6 in rise per 12 in run) is 26.57 degrees, and a 12 ft run at 30 degrees has a slope length of 13.86 ft.
Shingles are counted by the bundle: one bundle covers 33.33 sq ft and 3 bundles make one square (100 sq ft). With 10% waste, 1,732.05 sq ft of roof needs 58 bundles. Metal roofing is counted by the panel: a 40 ft eave with 3 ft wide panels needs 14 panels, each as long as the slope.
Related calculators: roof pitch, shingle and metal roofing.
Worked example: a 40 ft by 30 ft house with a 6/12 pitch
Take a house with a 40 ft by 30 ft footprint and a 6/12 roof pitch, and order shingles with the calculator’s usual 10% waste allowance. Here is the same maths the calculator does, step by step.
Step 1 – footprint area. The flat area under the roof is 40 x 30 = 1,200 sq ft. This is the number people usually get wrong, because it is not the roof area yet: a pitched roof has more surface than the floor plan below it.
Step 2 – pitch angle. The pitch angle comes from the rise and the run: a 6/12 pitch means 6 in of rise for every 12 in of run, and the angle is the inverse tangent of 6 / 12, which is 26.57 degrees.
Step 3 – roof area. Divide the footprint area by the cosine of the pitch angle. The cosine of 26.57 degrees is 0.89443, so the roof area is 1,200 / 0.89443 = 1,341.64 sq ft. That is one slope: the calculator counts a single roof slope here, so a simple gable roof, which has two slopes, is worked out in Step 6.
Step 4 – squares. One square of roofing is 100 sq ft, so 1,341.64 / 100 = 13.42 squares.
Step 5 – bundles. One bundle covers 33.33 sq ft, so without waste you would need 1,341.64 / 33.33 = 40.25 bundles. With the 10% waste allowance the calculator applies, that becomes 40.25 x 1.10 = 44.28, and you cannot buy part of a bundle, so the calculator rounds up to 45 bundles. The waste covers cuts at valleys, hips and ridges – use 15% on a cut-up roof.
Step 6 – both slopes. A simple gable roof has two slopes like this one, so the total roof area is 2 x 1,341.64 = 2,683.28 sq ft. Count the bundles again from that total, rather than just doubling the 45 bundles: 2,683.28 / 33.33 = 80.51, and with 10% waste that is 80.51 x 1.10 = 88.56, rounded up to 89 bundles.
If the roof is not a simple gable, work out each face on its own and add the areas together. Measure the footprint of each face, use the same pitch for the whole roof, and keep the waste allowance at 10% for a plain roof or 15% if the roof has hips, valleys and dormers. Measure each slope separately on a complex roof, add hips, valleys and overhangs, and confirm the final order with your roofer or supplier.
Roof area and shingle bundles for a 1,500 sq ft footprint
The table below uses the same method – footprint area divided by the cosine of the pitch angle, then bundles at 33.33 sq ft per bundle with the 10% waste allowance. It is for one slope of the roof. Steeper pitches make a much bigger difference than most people expect: a 10/12 roof has almost a quarter more surface than the same footprint at 4/12.
| Pitch | Pitch angle | Roof area | Bundles (10% waste) |
|---|---|---|---|
| 4/12 | 18.43 degrees | 1,581 sq ft | 53 |
| 6/12 | 26.57 degrees | 1,677 sq ft | 56 |
| 8/12 | 33.69 degrees | 1,803 sq ft | 60 |
| 10/12 | 39.81 degrees | 1,953 sq ft | 65 |
Metal roofing panels instead of shingles
For metal roofing, switch the calculator above to “Metal roofing – panels for an eave”. Panels run from the eave to the ridge, so each panel is as long as the slope, and the panel count is the eave length divided by the panel width, rounded up. This example uses the same house as the worked example above: 40 ft by 30 ft, with a 6/12 pitch and the usual 3 ft wide panels.
Step 1 – slope length. Half of the 30 ft width is a 15 ft run. At a 6/12 pitch the rise is 6/12 x 15 = 7.5 ft, so the slope length is the square root of 15 squared + 7.5 squared = 16.77 ft. Step 2 – panels for one slope. The eave is 40 ft long and each panel covers 3 ft, so 40 / 3 = 13.33, rounded up to 14 panels. Step 3 – panel length. Each of the 14 panels is 16.77 ft long, so the total for one slope is 14 x 16.77 = 234.8 linear ft, exactly as the calculator shows. Step 4 – both slopes. A simple gable roof has two slopes the same size, so order 28 panels in total, or 469.6 linear ft.
Add a spare panel for cuts and mistakes, as the calculator suggests, and confirm the panel width with your supplier before you order, because standing-seam panels can be narrower than the usual 3 ft.