Hip Rafter Length Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
A hip rafter length is calculated by multiplying the common rafter length by √2 (about 1.414), for a hip roof with four equally-pitched sides and right-angle corners.
Explanation
The hip rafter is the diagonal line formed where two sides meet on a hip roof (a four-sided roof), connecting the building's corner to the ridge point directly above it — unlike the common rafter, which runs perpendicular to the ridge on a standard two-sided roof. For a standard hip, with right-angle corners and the same pitch on all four sides, the hip rafter's ground projection forms the diagonal of a square whose side is the common rafter's ground projection: this diagonal equals exactly that side multiplied by √2 (about 1.414), a basic geometric property independent of the pitch. Once the same pitch is applied to that diagonal, the hip rafter's actual length is obtained directly by multiplying the common rafter's length (already sloped) by that same √2 factor — a classic carpentry rule, reproduced here as a calculator rather than a paper table. This length is then used to order the hip rafter beam or corresponding framing piece, usually of a larger cross-section than common rafters since it supports a wider roofing span on either side of the diagonal line — a structural sizing that still falls under a carpenter's or structural engineer's responsibility, this calculator giving only the piece's geometric length.
Example: 8 m span, 30% pitch
Inputs
Total building span: 8 m. Pitch: 30% on all four sides.
Calculation
Common rafter = (8 ÷ 2) ÷ cos(16.7°) ≈ 4.176 m. Hip rafter length = 4.176 × √2 ≈ 5.906 m.
Result
The hip rafter on this hip roof measures about 5.91 m.
Frequently asked questions
Does this formula work for a non-square rectangular building?
This √2 factor rule assumes a right-angle corner with a hip rafter oriented at 45° in plan, which is the standard case even on a rectangular building (the square forms locally at the corner, not across the whole building). It no longer applies as-is, however, if the two sides meeting at the hip have different pitches: that more complex case needs a specific trigonometric calculation, best left to a carpenter.
Why is the hip rafter longer than the common rafter?
Because in plan it travels along a diagonal (the straight-line distance between a building corner and the ridge point directly above it) rather than a simple segment perpendicular to the ridge: this diagonal is mechanically longer, by a factor of √2 for a right-angle corner, even before the pitch's slope is applied.
Is the hip rafter beam the same size as common rafters?
No, the hip rafter usually carries a wider roofing load (the hip jack rafters that bear against it on each side) and therefore most often needs a larger cross-section than common rafters. This structural sizing depends on the actual load and must be validated by a carpenter or structural engineer, this calculator giving only the piece's geometric length. The pitch itself, if not yet known, can be calculated directly with our roof pitch calculator from the building's height and span.