Hip Rafter Calculator
Reviewed by the My Roof Pitch editorial team · Updated · Free, no sign-up, works offline after first load
A hip rafter runs at a 45° plan angle, so its run per foot is 16.97 inches instead of 12. For a 24 ft square building at 6:12 with 2 ft overhangs, the hip run is 15.56 ft and the hip length is 17.42 ft. Jack rafters shorten by the common rafter spacing divided by 1.414 each step.
Your measurements
Enter the values you know — results update live.
For a square hip roof, the full width. For a rectangular plan, use the shorter end that forms the hip corner.
Enter 6 for a 6:12 roof.
Horizontal projection past the wall at each eave.
Analysis
Live results from your measurements.
Show the working
- Half span:
24 ÷ 2= 12 ft - Hip run:
(12 + 1.5) × √2= 19.092 ft - Hip rise:
19.092 × (6 ÷ 12)= 9.546 ft - Hip length:
√(19.092² + 9.546²)= 21.345 ft - Hip angle:
arctan(9.546 ÷ 19.092)= 19.47° - Side cut:
arctan(tan(26.57°) × cos(45°))= 19.47° - Jack count:
floor((12 + 1.5) ÷ 1.333)= 10 - Jack shorten:
1.333 × √2 × 1.118 × 12= 25.298 in
What this calculator does
A hip rafter is the diagonal member that runs from each corner of the building up to the ridge or peak of a hip roof. Because it sits at a 45° plan angle, its horizontal run is longer than the common rafter run by a factor of √2, and its slope is gentler than the common rafters. The side cut angle is the bevel needed where the hip meets the ridge or the common rafters, and the plumb cut is the vertical cheek cut at the ridge. Jack rafters are the shortened common rafters that fill the triangular spaces between the hip and the eaves; each one is shorter than the last by a fixed amount based on spacing and the hip geometry.
How to use it
- Measure the building span and halve it to get the common rafter run.
- Add the eave overhang, then multiply by √2 for the hip run.
- Multiply the hip run by the pitch ratio to get the hip rise.
- Take the square root of hip run squared plus hip rise squared for the hip length.
- Calculate the hip angle from the rise and run, then set plumb cut to 90° minus that angle.
- Lay out jack rafters at the common spacing, shortening each by the computed step length.
The formula
Hip run
hip run = (span / 2 + overhang) × sqrt(2)
The hip runs diagonally at 45°, so its plan length is √2 times the common run.
Hip rafter length
hip length = sqrt(hip run^2 + hip rise^2)
Pythagoras on the hip run and the hip rise, just like a common rafter.
Hip angle
hip angle = arctan(pitch / (12 × sqrt(2)))
The hip rises the same amount per foot of common run, but its own run is longer, so the angle is lower.
Jack rafter shorten
shorten = spacing × sqrt(2) × pitch multiplier
Each jack rafter is one spacing step back along the hip, measured along the slope.
Worked example
A 28 ft square hip roof at 8:12, 2 ft overhangs, jack rafters at 16 in centres.
- Half span: 28 ÷ 2 = 14 ft
- Hip run: (14 + 2) × 1.414 = 22.63 ft
- Hip rise: 22.63 × 0.6667 = 15.08 ft
- Hip length: √(22.63² + 15.08²) = 27.21 ft
- Hip angle: arctan(15.08 ÷ 22.63) = 33.69°
- Jack shorten: 1.333 × 1.414 × 1.2019 × 12 = 27.21 in
Cut the hip rafter at 27 ft 2 1/2 in, set the plumb cut to 56.31°, and shorten each jack rafter by 27.2 in.
Reference chart
| Pitch | Hip length per ft run | Angle | Side cut |
|---|---|---|---|
| 4:12 | 1.453 | 13.26° | 13.26° |
| 5:12 | 1.4743 | 16.42° | 16.42° |
| 6:12 | 1.5 | 19.47° | 19.47° |
| 8:12 | 1.5635 | 25.24° | 25.24° |
| 10:12 | 1.6415 | 30.51° | 30.51° |
| 12:12 | 1.7321 | 35.26° | 35.26° |
Hip rafter vs common rafter for a 24 ft span with 1.5 ft overhang
| Pitch | Common rafter | Hip rafter | Ratio |
|---|---|---|---|
| 4:12 | 12.65 ft | 17.89 ft | 1.414 |
| 6:12 | 13.42 ft | 18.97 ft | 1.414 |
| 8:12 | 14.42 ft | 20.4 ft | 1.414 |
| 10:12 | 15.62 ft | 22.09 ft | 1.414 |
| 12:12 | 16.97 ft | 24 ft | 1.414 |
Common mistakes
- Treating the hip rafter like a common rafter and using the same run.
- Forgetting the 45° plan angle; the hip run is √2 times the common run plus overhang.
- Cutting the hip plumb cut at the common roof angle instead of the gentler hip angle.
- Ignoring side cut bevel, which makes the hip meet the ridge and commons cleanly.
- Using the same shorten step for jack rafters on hips and valleys — valley geometry differs.
Assumptions and limits
- A square or regular hip roof with equal eave overhangs on all sides.
- The hip run is measured in plan view at 45° to the walls.
- Jack rafters are spaced at the same centre-to-centre spacing as common rafters.
- No ridge thickness deduction is applied to the hip; it lands against the commons or a short ridge block.
Frequently asked questions
How do you calculate hip rafter length?
Find the hip run by multiplying the common run plus overhang by √2, then multiply by the pitch multiplier. Or use Pythagoras: √(hip run² + hip rise²).
What is the difference between a hip rafter and a common rafter?
A common rafter runs perpendicular to the ridge. A hip rafter runs diagonally from a corner to the peak, so its plan run is longer and its angle is lower.
What angle do you cut a hip rafter?
The plumb cut is 90° minus the hip angle, which is arctan(pitch ÷ (12 × √2)). A 6:12 common roof gives a hip angle of about 19.47°, so the plumb cut is 70.53°.
How many jack rafters are on a hip roof?
Divide the common run plus overhang by the rafter spacing and round down. A 14 ft run with 16 in spacing gives 10 jack rafters per hip.
Why is the hip rafter deeper than a common rafter?
Because the hip supports more roof area and runs at a lower angle, it carries a larger tributary load. Many framers use one size deeper lumber or double up the hip.
What is a valley rafter?
A valley rafter is the inverse of a hip. It sits in an inside corner where two roof planes meet and carries water down to the eave. Its geometry is the same as a hip but the layout is reversed.
Related guides
Last updated 2026-08-05. Results are estimates for planning and are not a substitute for a licensed engineer or local code review.