How long is a hip rafter?

On a regular hip (the same pitch on both sides), the hip runs at 45° in plan, so its run is the common run × 1.414 and its length is the common run × √(2 + (pitch ÷ 12)²). A 12 ft common run at 6/12 gives an 18 ft hip line length — the 6/12 hip factor is exactly 1.5.

What pitch is the hip itself?

The hip rises the same as the common but over 16.97 in of run for every 12 on the common, so a 6/12 roof has a 6-in-16.97 hip, about 19.5° from level. On a framing square you set the plumb cut at 6 and 17 for a 6/12 hip.

What is the common difference for jack rafters?

How much shorter each jack is than the one before, at your layout spacing: spacing × √(1 + (pitch ÷ 12)²). At 16 in centres on a 6/12 roof it is 16 × 1.118 ≈ 17 7/8 in. Cut the longest jack, then take the common difference off each next one.

Are these the lengths I cut?

They are line lengths — building line to the centre of the ridge, on the rafter's measuring line. Shorten the common by half the ridge thickness (measured level), and the hip by half the ridge's 45° thickness, then add the overhang. Size the lumber from your span tables or engineer: this is geometry, not structure.

Hip & valley rafter calculator

Geometry for a regular hip or valley — both roof planes at the same pitch. It does not size the hip, the jacks or the ridge: that comes from your span tables, your plans or an engineer.

Type the common run and the pitch. The calculator gives the hip (or valley) line length, the hip's own pitch for the plumb cut, the common rafter length, and the common difference that shortens each jack rafter at your layout spacing — the four numbers a framer needs before cutting a hip roof.

Worked example

A 24 ft wide building, so a 12 ft common run, at 6/12. The common is 12 × √(1 + 0.5²) = 12 × 1.118 = 13.42 ft (13′ 5″). The hip is 12 × √(2 + 0.5²) = 12 × 1.5 = 18 ft. The hip rises 6 over 16.97, so its plumb cut is atan(6 ÷ 16.97) = 19.5° from level. At 16 in centres the jacks shorten by 16 × 1.118 = 17 7/8 in each. A 1 ft level overhang adds 1.12 ft to each common and 1.5 ft to each hip.

Try one

Quick referencefor regular hips

Common: run × √(1 + (pitch ÷ 12)²)
Hip / valley: run × √(2 + (pitch ÷ 12)²) · run in plan = run × 1.414
Hip per foot of common run: 4/12 17.44 in · 5/12 17.69 in · 6/12 18.00 in · 8/12 18.76 in · 10/12 19.70 in · 12/12 20.78 in
Hip plumb cut: pitch over 16.97 (17 on the square) · 6/12 → 6 and 17 · 12/12 → 12 and 17
Jack difference: spacing × √(1 + (pitch ÷ 12)²) · 16 in at 6/12 = 17 7/8 · 24 in at 6/12 = 26 13/16

The formula

common = run·√(1 + t²) · hip = run·√(2 + t²) · hip angle = atan(t ÷ √2) · t = pitch ÷ 12

The hip sits over the diagonal of a square whose side is the common run, so its run is √2 times longer while it climbs the same height. Everything else is the same right triangle the common rafter uses.

Questions

How long is a hip rafter?: On a regular hip (the same pitch on both sides), the hip runs at 45° in plan, so its run is the common run × 1.414 and its length is the common run × √(2 + (pitch ÷ 12)²). A 12 ft common run at 6/12 gives an 18 ft hip line length — the 6/12 hip factor is exactly 1.5.
What pitch is the hip itself?: The hip rises the same as the common but over 16.97 in of run for every 12 on the common, so a 6/12 roof has a 6-in-16.97 hip, about 19.5° from level. On a framing square you set the plumb cut at 6 and 17 for a 6/12 hip.
What is the common difference for jack rafters?: How much shorter each jack is than the one before, at your layout spacing: spacing × √(1 + (pitch ÷ 12)²). At 16 in centres on a 6/12 roof it is 16 × 1.118 ≈ 17 7/8 in. Cut the longest jack, then take the common difference off each next one.
Are these the lengths I cut?: They are line lengths — building line to the centre of the ridge, on the rafter's measuring line. Shorten the common by half the ridge thickness (measured level), and the hip by half the ridge's 45° thickness, then add the overhang. Size the lumber from your span tables or engineer: this is geometry, not structure.

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