Free Hip Roof Tool

Roof Pitch Hip Calculator

This roof pitch hip calculator determines hip rafter length, hip rafter angle, jack rafter lengths, and compound miter cuts for hip roof framing. A hip roof slopes on all four sides, requiring specialized angle calculations that differ from common rafters. For a 6:12 pitch, the hip rafter drops at 4.24:12 (the diagonal pitch), and the hip rafter length is 1.5× the common rafter length. The calculator provides all framing dimensions needed for accurate hip roof construction.

architecture Hip Roof Framing Diagram

RIDGE HIP HIP Common Rafters
Hip Pitch4.24:12
Hip Angle19.5°
Hip/Common Ratio1.414×
architecture Hip Roof Inputs
ft
: 12
assessment Hip Rafter Results
Common Rafter Length—
Hip Rafter Length—
Hip Rafter Pitch—
Common Plumb Angle—
Hip Plumb Angle—
Jack Rafter Difference—

How to Calculate Hip Roof Pitch

Hip roof calculations start with the common rafter pitch, then derive the hip rafter pitch using the Pythagorean theorem applied to the diagonal. The hip rafter travels at 45° in plan view, creating a lower effective pitch than the common rafters.

tune Drag the Slider to Change Pitch
Run Rise Slope 26.57°
0.5:12 24:12
Angle 26.57°
Grade 50.0%
Multiplier 1.118
Type Conventional
1
straighten

Determine Common Pitch

2
architecture

Calculate Hip Rafter Pitch

3
calculate

Compute Hip Rafter Length

Hip Roof Formulas

Essential formulas for hip rafter and jack rafter calculations:

straighten Hip Rafter Length
Hip = Common Rafter × √2
13.42 ft × 1.414 = 18.97 ft hip rafter (at 6:12)
rotate_right Hip Rafter Pitch
Hip Pitch = Common Pitch ÷ √2
6:12 ÷ 1.414 = 4.24:12 hip rafter pitch
percent Jack Rafter Spacing
Jack Diff = OC Spacing × Pitch Multiplier
16" OC × 1.118 (6:12) = 17.89" jack difference
science Live Formula Calculator
ft
ft
Pitch 6 : 12
Angle 26.57°
Grade 50.0%
Rafter 13.42 ft
Multiplier 1.118

Hip Rafter Reference Chart

Click any row to see the pitch angle visualized. The chart covers all standard pitches from flat (1:12) to steep (12:12) with walkability ratings, material compatibility, and snow shedding performance.

Pitch Angle Grade Multiplier Type Walkability Snow Shedding
1:12 4.76° 8.3% 1.003 Flat/Low Easy Poor
2:12 9.46° 16.7% 1.014 Low Slope Easy Poor
3:12 14.04° 25.0% 1.031 Low Slope Easy Fair
4:12 18.43° 33.3% 1.054 Conventional Easy Fair
5:12 22.62° 41.7% 1.083 Conventional Easy Good
6:12 26.57° 50.0% 1.118 Conventional Moderate Good
7:12 30.26° 58.3% 1.158 Conventional Caution Very Good
8:12 33.69° 66.7% 1.202 Conventional Caution Very Good
9:12 36.87° 75.0% 1.250 Steep Unsafe Excellent
10:12 39.81° 83.3% 1.302 Steep Unsafe Excellent
11:12 42.51° 91.7% 1.357 Steep Unsafe Excellent
12:12 45.00° 100.0% 1.414 Steep Unsafe Excellent
6:12 — 26.57°
Compatible: All Types

FAQs

Answers to the 14 most common questions about roof pitch, slope angle, walkability, snow load, and roofing materials.

What is a hip rafter on a roof?

A hip rafter is the diagonal structural member that runs from the wall corner to the ridge at a 45° angle in plan view. It forms the external angle where two sloping roof planes meet. Hip rafters are longer and set at a shallower pitch than common rafters.

How do you calculate hip rafter length?

Hip rafter length = common rafter length × √2 (1.414). For a building with a 12 ft (3.66 m) run and 6:12 pitch: common rafter = 13.42 ft, hip rafter = 13.42 × 1.414 = 18.97 ft (5.78 m).

What angle do you cut a hip rafter?

A hip rafter requires a compound cut combining the plumb cut and a 45° cheek cut. For a 6:12 pitch: the plumb cut angle is 23.2° (hip pitch), and the cheek cut is 45° to sit against the ridge. Use a framing square set at 4.24 and 12.

What is the difference between hip and valley rafters?

Hip rafters form external (convex) angles; valley rafters form internal (concave) angles. Both are calculated identically — using the common pitch ÷ √2 — but valley rafters sit in the interior angle where two roof planes meet.

How long are jack rafters on a hip roof?

Jack rafters decrease in length uniformly from the common rafter to the hip corner. Each jack is shorter by the 'jack rafter difference' = OC spacing × common rafter pitch multiplier. At 16" OC and 6:12 pitch, each jack is 17.89 inches shorter.

Is a hip roof stronger than a gable roof?

Yes, hip roofs are generally stronger in wind resistance. The four sloping sides create a self-bracing structure. Hip roofs receive better wind resistance ratings from insurance companies and typically perform 15–20% better in hurricane-force winds compared to gable roofs.