Hip Roof Framing Geometry

Total wall-to-wall width (Common Run = Span / 2).
e.g. 6 = 6/12 pitch (26.57°).

Hip & Valley Rafter Calculator — Lengths, Plumb Cuts & Set-Out

Calculation Results & Roof Elevation Blueprint

Scaled 2D common and hip rafter elevation plan blueprint, plumb/seat cut angles, and jack rafter differences:

🏠 Hip Roof Rafter & Plan Blueprint
Hip Rafter Blueprint Scaled 2D roof elevation showing common rafter, ridge board, wall plate bird's mouth, and pitch triangle.
Common Rafter Length
13 ft 5 in
Plumb Cut: 26.57°
Hip Rafter Length
18 ft 0 in
Hip Plumb Cut: 19.47°
Jack Common Difference
17-7/8 in
Shortens per 16" o.c. spacing
Hip Cheek & Backing Cuts
43.32°
Backing Bevel: 18.43° (Square Mark: 11.5)

📐 Rafter Cut & Running Set-Out Specification Matrix

Framing dimensions and saw cut angles for common, hip, and jack rafters:

Framing Member Theoretical Length Plumb Saw Cut Seat Cut Angle

📦 Hip Roof Timber & Rafter Bill of Materials (BOM)

Select Item Description Est. Quantity Material Specification

Related Roof Framing Calculators

📋 Informational Code Check — IRC R802 Rafter Framing

IRC R802.3 Ridge & Hip Depth: Hip rafters must be supported and cut with depth equal to or exceeding the cut end of common rafters (minimum 2" nominal stock thickness).

Slope Limit: Asphalt shingle roofing requires a minimum slope of 2:12 (9.46°); pitches below 4:12 require double underlayment per IRC R905.2.2.

⚠️ Compliance Notice: This Code Check is informational for layout planning. It is not a substitute for an official permit, building code inspection, or structural engineer certification. Always verify lumber species grade and design loads with your local building department.

📐 Module 7: Worked Example & Math Proof

Problem Statement: Calculate common rafter, hip rafter, backing bevel, and cheek cut angle for a building span $W = 24.0\text{ ft}$ ($288\text{ in}$) with a $6/12$ roof pitch ($26.57^{\circ}$).

  • Common Run: $R_{\text{common}} = 288 / 2 = 144\text{ in}$
  • Common Rafter Length: $L_{\text{common}} = 144 \times \sqrt{1 + (6/12)^2} = 144 \times 1.11803 = 161.00\text{ in}$ ($13\text{ ft } 5\text{ in}$)
  • Hip Rafter Length: $L_{\text{hip}} = 144 \times \sqrt{1 + 1 + (6/12)^2} = 144 \times 1.5000 = 216.00\text{ in}$ ($18\text{ ft } 0\text{ in}$)
  • Jack Rafter Difference: $\Delta_{\text{jack}} = 16.0 \times 1.11803 = 17.89\text{ in}$ on $16\text{ in}$ center spacing
  • Hip Backing Bevel: $\theta_{\text{backing}} = \arccos(\cos(26.57^{\circ}) / \cos(19.47^{\circ})) = 18.43^{\circ}$
  • Cheek Cut Angle: $\theta_{\text{cheek}} = \arctan(17 / \sqrt{289 + 36}) = 43.32^{\circ}$

🧰 Module 8: Jobsite Tools, PPE & Framing Pitfalls

Required Tools & PPE

  • Framing square with stair gauges
  • Adjustable bevel gauge & protractor
  • 7-1/4" circular saw with 24T framing blade
  • ANSI Z87.1 safety glasses & hearing protection

Pro Framing Pitfalls

  • Ridge Deduction: Forgetting to deduct half the ridge thickness (0.75" for 2x stock) perpendicular to the plumb cut.
  • Cheek vs Plumb: Misreading the compound cheek miter for the plumb cut angle on bevel saws.
  • Lumber Crown: Cutting hip rafters with the crown facing down causing sagging roof valleys.

Module 9: Related Roofing & Framing Tools

Module 10: Frequently Asked Questions (15 FAQs)

What is the length of a hip rafter for a 24 ft span with 6/12 pitch?

For a 24 ft building span (144 in run) at 6/12 pitch, the unadjusted hip rafter length is exactly 216.00 inches (18 ft 0 in).

What is the hip backing bevel angle for a 6/12 roof pitch?

The backing bevel angle for a regular equal-pitch 6/12 hip roof is 18.43°.

What is the cheek cut angle for a 6/12 hip rafter?

The side cheek cut angle (side cut angle) for a 6/12 hip rafter is 43.32° (side cut number 11.5 on a framing square).

What is the jack rafter length difference on 16 in centers for a 6/12 pitch?

On 16 in center spacing, each consecutive jack rafter decreases in length by 17.89 inches (1 ft 5-7/8 in).

Why is a hip rafter longer than a common rafter?

A hip rafter runs diagonally across the corner of the building at a 45° plan angle, so its horizontal run is 16.97 in per foot of common run rather than 12 in.

How do you deduct for the ridge board thickness on a hip rafter?

Deduct half the 45° diagonal thickness of the ridge stock (e.g. 1.06 in for a 1.5 in thick ridge) along the rafter run line before marking the plumb cut.

What size lumber is required for hip rafters under IRC R802.3?

IRC Section R802.3 requires hip rafters to be cut from stock at least 2 in nominal thickness, with depth equal to or exceeding the cut end of common rafters.

What is a hip backing bevel?

A backing bevel is a chamfer cut along the top edge of a hip rafter so roof sheathing sits flush on both intersecting roof planes.

How do you calculate hip rafter plumb cut angle?

Plumb cut angle $\theta_{\text{hip}} = \arctan(\text{rise} / 16.9706)$. For a 6/12 pitch, the hip plumb cut is 19.47°.

What is the difference between a hip rafter and a valley rafter?

A hip rafter forms an outside convex ridge corner, whereas a valley rafter forms an inside concave trough corner where two roof planes meet.

Does a flat roof (0/12 pitch) have a cheek cut angle?

Yes, for a flat 0/12 pitch corner intersection, the cheek cut angle is exactly 45.00° and the backing bevel is 0.00°.

What is the jack rafter difference on 24 in centers for 6/12 pitch?

On 24 in spacing, each consecutive jack rafter decreases by 26.83 inches (2 ft 2-7/8 in).

How do you mark a bird's mouth on a hip rafter?

Mark the seat cut using the hip unit run (16.97 in) and pitch rise, ensuring remaining throat depth is at least two-thirds of the board width.

What hurricane ties are used for hip rafters?

Skewed hurricane ties (such as Simpson Strong-Tie H10S or LSU) rated for 45° corner hips must be used to meet wind uplift codes.

Can hip rafters be engineered LVL instead of dimensional lumber?

Yes, engineered Laminated Veneer Lumber (LVL) is commonly specified for long hip rafter spans to prevent sag and warping.

Sources & Governing Codes

  1. IRC 2021 Section R802 Roof Construction Standard: IRC 2021 Section R802 Roof Construction Standard View Standard
  2. IRC 2021 Section R802.3 Rafter & Ridge Specifications: IRC 2021 Section R802.3 Rafter & Ridge Specifications View Standard
  3. IRC 2021 Section R802.4 Allowable Rafter Spans Table: IRC 2021 Section R802.4 Allowable Rafter Spans Table View Standard
  4. IRC 2021 Section R905.2 Asphalt Shingles Assembly Code: IRC 2021 Section R905.2 Asphalt Shingles Assembly Code View Standard
  5. IRC 2021 Section R905.10 Metal Roof Panel Code: IRC 2021 Section R905.10 Metal Roof Panel Code View Standard
  6. AWC Wood Frame Construction Manual (WFCM): AWC Wood Frame Construction Manual (WFCM) View Standard
  7. AWC National Design Specification (NDS): AWC National Design Specification (NDS) View Standard
  8. USDA Forest Products Laboratory Wood Handbook (FPL-GTR-282): USDA Forest Products Laboratory Wood Handbook (FPL-GTR-282) View Standard
⚠️ Rafter Layout & Roof Code Safety Disclaimer: Rafter calculations are a layout aid for regular equal-pitch hip roofs. Always verify rafter sizing, span tables, ridge support beams, and hurricane tie connections against local building codes (IRC Section R802) and a licensed structural engineer before cutting lumber.