Plan area times the pitch factor
A roof covers more area than the floor plan under it because it slopes. The relationship is fixed by the pitch: the true area is the plan area divided by the cosine of the pitch angle. That works for every simple roof, gable or hip, because every plane of the roof slopes at the same angle. Include the eaves in the plan, since they are roofed too.
true area = plan area ÷ cos(pitch) rafter length = horizontal run ÷ cos(pitch)
| Pitch | Factor | 160 m² plan becomes | Typical of |
|---|---|---|---|
| 5° | 1.004 | 160.6 m² | Low skillions |
| 15° | 1.035 | 165.6 m² | Modern low-pitch |
| 22.5° | 1.082 | 173.2 m² | Most project homes |
| 25° | 1.103 | 176.5 m² | Tiled roofs |
| 30° | 1.155 | 184.8 m² | Older homes, steep tiles |
| 45° | 1.414 | 226.3 m² | Attic roofs |
Gable, hip and skillion
For the same plan and pitch, a gable roof and a hip roof have the same area. What changes is the lengths. A gable has a ridge the full length of the building and four barges running down the gable ends, with gutter along the two long sides. A hip roof has a shorter ridge, the length minus the width, four hips running diagonally from each corner up to the ridge ends, no barges, and gutter all the way round. A skillion is one plane across the whole width, with a gutter on the low side and a barge at each end. The calculator switches the lengths as you change the type.
Hips are the length people get wrong. A hip rafter runs diagonally, so its horizontal run is the half-width times the square root of two, and its length is found from that run and the rise. On a 10.9 m wide roof at 22.5 degrees the half-width is 5.45 m, the rise 2.26 m, and each hip is 8.0 m long.
Squares
Roofers and estimators still talk in squares, an imperial unit of 100 square feet, which is 9.29 m². A 173 m² roof is about 18.6 squares. Tile and sheet suppliers have long since gone metric, but the word survives in quotes and it is useful to know the conversion.
Complex roofs
A roof with a wing, a dormer or two different pitches is several simple roofs joined together. Work each plane or each rectangle of plan on its own, with its own pitch, and add them. Valleys, where two planes meet in a trough, need valley gutter and extra flashing, and their length is found the same way as a hip.
Worked example
A 15 × 10 m house with 450 mm eaves and a hip roof at 22.5 degrees. Plan with eaves 15.9 × 10.9 = 173.3 m². Pitch factor 1.082, so the true area is 187.6 m², about 20 squares. Rafter length from gutter to ridge 5.9 m, rise 2.26 m. Ridge 15.9 − 10.9 = 5.0 m. Four hips of 8.0 m, 32 m in total. Gutter and fascia 53.6 m all round. Change to a gable and the area stays 187.6 m², the ridge becomes 15.9 m, the hips disappear, barges total 23.6 m and the gutter drops to 31.8 m.
Common questions
How do I get roof area from the floor plan?
Plan area including eaves, times 1 ÷ cos(pitch). At 22.5° that is × 1.082.
What is a roofing square?
100 square feet, 9.29 m².
How long is a hip rafter?
Square root of (horizontal diagonal run² + rise²). About 8 m on a 10.9 m wide roof at 22.5°.
Hip vs gable area?
The same for the same plan and pitch. Only the ridge, hips and barges differ.
Geometry for simple roofs. Structural member sizes, tie-downs and wind classification come from AS 1684, the truss designer or the engineer.