About this calculator
Estimates the quantities for a simple, uniformly-pitched full hip roof (every slope at the same pitch, hip lines at 45° in plan): ridge length, common/hip/jack rafter counts and lengths, and covering area with waste. A half-hip, Dutch-gable, or unequal-pitch hip roof is out of scope.
Formula
d = building width / 2 + eaves overhang
ridge length = building length − building width (0 = a pyramid hip roof)
common rafter length = d / cos(pitch)
common rafter count = ceil(ridge length / spacing) + 1 (0 when ridge length = 0)
hip rafter length = d × √(2 + tan²(pitch))
hip rafter count = 4 (always)
jack rafter positions per face = ceil((width/2) / spacing) − 1
jack rafter count = 8 × jack positions (4 corners × 2 adjoining faces)
jack rafter length at position n = (n × spacing) / cos(pitch)
total covering area = (length + 2×eaves) × (width + 2×eaves) / cos(pitch)
covering area (incl. waste) = total area × (1 + waste% / 100)
Because a hip's 45° plan angle means advancing a given distance perpendicular to the eave
requires travelling √2 times that distance along the hip, while the vertical rise depends
only on the perpendicular distance (the roof is one continuous plane), the hip rafron length
works out to d × √(2 + tan²(pitch)) — a right-triangle decomposition, not a rule of thumb.
The same reasoning gives each jack rafter's run, and hence length, as if it were a common
rafter of a shorter run.
Total covering area uses a general identity for any uniformly-pitched roof: the inclined surface area equals the horizontal projected area (including the overhang) divided by cos(pitch), regardless of the individual slopes' plan shapes.
Worked example
Defaults: 10 m × 6 m building, 45° pitch, no overhang, 600 mm rafter spacing, 10% waste.
d = 3 m; ridge length = 10 − 6 = 4 m
common rafter length = 3 / cos(45°) = 3√2 ≈ 4.243 m
common rafter count = ceil(4000/600) + 1 = 8
hip rafter length = 3 × √(2 + 1²) = 3√3 ≈ 5.196 m
jack positions per face = ceil(3000/600) − 1 = 4 → 32 jack rafters total
total area = (10×6) / cos(45°) = 60√2 ≈ 84.85 m²; incl. waste ≈ 93.34 m²
FAQ
What if the building isn't a simple rectangle, or the pitches differ? This calculator only covers a uniformly-pitched, simple rectangular-plan full hip roof. A half-hip, Dutch gable, or a hip roof with different pitches on different sides needs its own take-off — the formulas here don't apply.
Why is "width equals length" allowed? That's a pyramid hip roof (four equal triangular faces meeting at a point) — a valid special case with a zero-length ridge and no common rafters, only hip and jack rafters.
Why doesn't the calculator cite a standard?
No standard was found covering hip roof quantity take-off; the geometry here is
trigonometry, not a building-code requirement, so meta.standards is left empty.
Assumptions and limits
Assumes a uniform pitch on every slope and 45° hip lines in plan (the standard case for a rectangular building). Rafter and hip sizing, connections, and bracing are not checked — this is a quantity take-off only; structural design must be verified by a qualified engineer.