Hip Rafter Calculator

Compare the common rafter and the diagonal hip rafter for the same run and pitch, with both angles to the horizontal.

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A hip rafter runs from the corner of the building diagonally up to the end of the ridge. Because it travels at 45 degrees in plan on a regular hip, its horizontal plan run is the common run times √2. It climbs the same vertical rise as the common rafter, so it is longer but not simply the common length times √2.

Common run vs. diagonal plan run

For a common run R and pitch p: the common length is R × √(1 + p²); the hip plan run is R × √2; and the hip length is R × √(2 + p²). The common angle to the horizontal is arctan(p), while the hip angle is arctan(p / √2), which is always shallower because the hip covers more horizontal distance for the same rise.

Angles are geometric, not saw settings

The angles here are geometric angles to the horizontal. They are not backing bevels, cheek-cut angles or compound saw settings. Producing those requires a separate, documented cutting model and attention to the physical thickness of the hip, so this tool deliberately stops at the line geometry. For the straight runs use the common rafter calculator.