Rules · Roofs · Materials · Site
Pitch a roof no lower than its covering allows (roughly 45° for thatch, 35° for plain tiles, 20–25° for slate, 15–20° for interlocking tiles, a few degrees for sheet metal) and steeper where snow lies long or rain is heavy.
thatch ≥ 45° · plain tile ≥ 35° · slate ≥ 22½° · pantile ≥ 17½° · metal ≥ 5° · membrane ≈ 1–2°
Viollet-le-Duc explained the roofs of medieval France by the materials that covered them: the flat, overlapping tiles and slates of the north demanded steep pitches, the curved Roman tiles of the Mediterranean lie happily on low ones. Climate reinforces material. Heavy snow slides off a steep roof before its weight becomes dangerous, and driving rain is kept out by the greater overlap a steep slope allows; in a hot dry country a flat roof is a cool terrace for sleeping.
The figures given here are rounded modern guidance; the exact minimum depends on the lap, the exposure and the underlay.
Cover a wide nave with triangulated timber trusses rather than a vault: their tie-beams take the outward thrust, so the walls need only carry weight and may stand on slender columns.
nave span ≈ 13–24 m on trusses (Santa Sabina ≈ 13.5 m; Old St Peter’s ≈ 24 m)
For a great hall, measure the distance between the front and back eave purlins and raise the ridge purlin above them by one third of it; for lesser halls, by about a quarter.
rise = ⅓ × depth between eave purlins (halls); ≈ ¼ (+ a small addition) for ting-tang halls
Draw a straight line from the ridge purlin to the eave purlin and lower the first purlin below the ridge from it by one tenth of the rise; from that point draw a new line to the eave purlin and lower the next purlin by one twentieth; continue, halving each time.
drop₁ = H⁄10 · drop₂ = H⁄20 · drop₃ = H⁄40 · …
Give each rafter span a fixed slope, increasing from the eaves to the ridge: half-pitch (5 jǔ) for the eave span, then about 6½ or 7, 7½, and 9 tenths for the span below the ridge.
rise of span k = run × (0.5, 0.65, 0.75, 0.9) for four spans
From the intermediate bracket set of the second bay the rafter ends advance progressively outward, so that at the corner the eave projects further (by 4 cun for a hall of one bay, 5 for three bays, 7 for five bays) and rises with the corner beam.
Give the hipped roof (wudian) to the highest halls, the hip-and-gable (xieshan) to the next, and the gabled roofs, overhanging (xuanshan) and flush (yingshan), to lesser buildings and houses; double the eaves for the very highest.
double wudian > double xieshan > wudian > xieshan > xuanshan > yingshan
Cite this page Chris Paton, “Each covering has its lowest pitch”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/roof-pitch-covering. Text, drawings and models licensed under CC BY-NC 4.0.