Roof geometry
Duo-pitch (gable) roof: area, eaves, verge and gable triangle
- where
- slope length, eaves to ridge (m)
- horizontal span, eaves to eaves (m)
- roof pitch (°)
- roof area, both slopes (m²)
- roof length along the ridge (m)
- eaves length, both slopes (m)
- total verge length (m)
- number of gable verges (ends)
- area of each gable triangle (m²)
Explain this equation
Takes off the main quantities for a simple gable roof: the covered area, the eaves and verge lengths, and the triangle of gable wall under each verge. Use it for pricing tiles, fascia, verge trim and gable brickwork or cladding.
Half the span S divided by cos p is the slope length L_s from eaves to ridge. Two slopes of length L give the area. Each gable end has a verge up both sides, so the verge total is 2 n_g L_s. The gable triangle has a base of S and a height of half the span times tan p.
Everything comes from the right-angled triangle formed by half the span, the rise and the rafter. The triangle area is half base times height, which simplifies to S² tan p / 4.
Sense check: a 10 m long, 8 m span roof at 35° has slopes of about 4.88 m, about 97.7 m² of roof and gable triangles of about 11.2 m² each.
Watch out: put the overhangs into L and S if you want them in the area, and leave n_g at 0 for ends that are hipped or abut another wall.
Quantities for a plain duo-pitch roof: the covered area, eaves run, verge run and the triangular gable area above the eaves line. Ridge length is the roof length.
Enter your values to see the result.
Good to know
Enter the lengths that get covered: verge to verge including any verge overhang, and eaves to eaves including the overhang. The gable triangle uses the same span, so for brickwork or tile-hanging on the gable wall itself enter the wall span instead. One gable end has two verges (one per slope). Enter 1 gable for a roof hipped or abutting at the other end.
Common mistake
Counting one verge per gable. Each gable has a verge on each slope, so a two-gable roof has four verge lengths.
Limits
Symmetrical, equal-pitch roof with a horizontal ridge. Valleys, hips and dormers need the other calculators.
Sources
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the roof covering manufacturer’s fixing specification, BS 5534, BS 8000-6, BS 6229, the Lead Sheet Training Academy guidance and Building Regulations. Wind uplift and structural design need a competent designer.