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A roof rises its pitch in inches for every foot of horizontal run. On a gable or hip roof the run is half the building width and on a shed roof it is the full width, so a 30 ft wide gable at 6/12 rises 15 × 6 ÷ 12 = 7.5 ft from the wall plate to the ridge. The Roof Height Calculator adds the wall height and the heel (the rafter or truss height above the plate) to give the eave and ridge heights, the mean roof height used for wind design under ASCE 7 section 26.2 (the average of the eave and ridge heights, or the eave height for roofs of 10° or less), the rafter length and the volume of the attic. A 40 × 30 ft gable at 6/12 on 9 ft walls with a 4 in heel has its ridge at 16 ft 10 in, a mean roof height of 13.08 ft and 4,500 cu ft of attic; the hip version of the same roof encloses 3,375 cu ft.
A roof rises its pitch in inches for every foot of run. The run is half the building width for a gable or hip roof and the full width for a shed roof. Add the wall height and the heel — the rafter or truss height above the wall plate — for the height above the floor or grade.
| Width | 4/12 | 6/12 | 8/12 | 10/12 | 12/12 |
|---|---|---|---|---|---|
| 20 ft | 3.33 ft | 5.00 ft | 6.67 ft | 8.33 ft | 10.00 ft |
| 24 ft | 4.00 ft | 6.00 ft | 8.00 ft | 10.00 ft | 12.00 ft |
| 28 ft | 4.67 ft | 7.00 ft | 9.33 ft | 11.67 ft | 14.00 ft |
| 30 ft | 5.00 ft | 7.50 ft | 10.00 ft | 12.50 ft | 15.00 ft |
| 36 ft | 6.00 ft | 9.00 ft | 12.00 ft | 15.00 ft | 18.00 ft |
| 40 ft | 6.67 ft | 10.00 ft | 13.33 ft | 16.67 ft | 20.00 ft |
ASCE 7 (section 26.2) defines mean roof height as the average of the eave height and the height of the highest point on the roof; for roofs of 10° or less it may be taken as the eave height. It is the height at which wind pressures are read for the building.
Multiply the horizontal run by the pitch and divide by 12. For a gable or hip roof the run is half the building width; for a shed roof it is the full width. A 30 ft wide house at 6/12 rises 15 × 6 ÷ 12 = 7.5 ft from the wall plate to the ridge. Add the wall height and the heel (the rafter or truss height above the plate) for the height above the floor or ground.
Half a foot of rise for every foot of run. A 24 ft wide gable rises 6 ft, a 30 ft gable 7.5 ft and a 40 ft gable 10 ft above the plate. A 12/12 roof rises twice as much — 15 ft on a 30 ft span.
The wind-load height used by ASCE 7 (section 26.2): the average of the eave height and the height of the highest point on the roof. For roofs of 10 degrees or less it may be taken as the eave height. With 9 ft 4 in to the eave and 16 ft 10 in to the ridge, the mean roof height is about 13 ft 1 in.
No — at the same pitch over the same width, a hip and a gable reach the same ridge height. The hip roof encloses less attic volume because its ends slope in: over a 40 × 30 ft house at 6/12 the gable attic is 4,500 cu ft and the hip attic 3,375 cu ft.
For a gable or shed roof, multiply the triangular cross-section (width × rise ÷ 2) by the length. For a hip roof, add a triangular prism for the part of the ridge longer than the width and a pyramid for the two hipped ends: (W × h ÷ 2) × (L − W) + W² × h ÷ 3.
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