A 40 × 28 ft house with a 6/12 hip roof and 12 in eaves has a 12 ft ridge, four 22 ft 6 in hip rafters and 1,409 square feet of roof: 15.5 squares with waste. It takes 106 rafters at 16 in on center: 20 commons along the ridge, one central rafter at each end, four hips and 80 jacks. The calculator above works out hip and pyramid roofs of any size, with the rafter check and the materials.
How the calculator works
Enter the building length and width, the pitch and the eave overhang. The ridge runs along the longer side. Tick “Pyramid roof” for a roof whose four slopes meet at one point. Then the rafters, the lumber, the snow load and the covering.
Geometry
On a hip roof every slope has the same pitch, so the ridge is as long as the length minus the width: 40 − 28 = 12 ft. Each hip runs from a corner of the eaves up to an end of the ridge. With equal pitches the roof area is simply the plan area including the overhangs times the slope factor: 42 × 30 × 1.118 = 1,409 ft². The two long slopes are trapezoids and the two ends triangles; their sloped heights are measured along the middle of each face, not along the hip.
A pyramid roof on a rectangular building has no ridge. Its end slopes are flatter than its long slopes, because they rise to the same peak over a longer run, and the end overhang is longer so the eave stays at one level all round. The calculator shows both slopes.
Rafters
Common rafters run from the eaves up to the ridge at the spacing, one more than the spaces. At each end a central rafter runs up to the end of the ridge. The four hips carry jack rafters on both sides; each jack is one spacing shorter than the last, so their total length falls quickly toward the corners. The calculator adds up every jack. Hips are at least as deep as the cut ends of the jacks that frame into them (IRC R802.4.3), which on a sloped cut means one size deeper than the commons: 2x10 hips for 2x8 rafters.
| Default roof, 16 in o.c. | Count |
|---|---|
| Common rafters | 20 |
| End central rafters | 2 |
| Jack rafters | 80 |
| Hip rafters (22' 6") | 4 |
Is the rafter big enough?
The common rafter is checked by the AWC span method for the lumber, the spacing and the loads; its span is the horizontal run, half the building width. A 2x8 Douglas fir-larch No. 2 at 16 in spans 14 ft 5 in under 30 psf of snow and a 15 psf shingle roof, and the run here is 14 ft. Hip rafters carry the jacks and in larger roofs are often engineered beams; the calculator gives their length and the minimum depth.
Materials
Covering adds 10 % for shingles, metal and tile, 15 % for shakes; hip roofs have more cut pieces than gables, so stay on the generous side. OSB or plywood sheathing is counted in 4 × 8 ft sheets with 8 % for the angled cuts along the hips. Drip edge and gutters run along all four eaves, 144 ft here, and hip and ridge caps along the hips and the ridge.
Common mistakes
- Measuring the hip end as a triangle with the hip length as its height. The height of the end face is its slant height up the middle, shorter than the hip; using the hip overstates the area.
- Counting jacks on one side of each hip. There are jacks on both sides.
- Same depth hips and commons. The hip must be at least as deep as the jacks' cut ends.
For a gable roof, use the Rafter Length Calculator; for the span of any rafter, the Rafter Span Calculator.