Hip & Valley Rafter Length (√(144+144+Rise²)/12), Jack Rafter Decrement & Backing Angle Calculator

Compute Common, Hip/Valley, and Jack rafter lengths and compound cheek cut angles.

Hip / Valley Rafter Line Length
21 ft (252 in)
Common Rafter Line Length 15.65 ft
Jack Rafter Difference (@ 16" OC) 17.89 inches
Hip Rafter Plumb Pitch Angle 19.47 degrees
Inputs
⚡ Scenarios:
ft
Total exterior building width (span = 2 × common run) in feet.
in/12
Roof pitch rise in inches per 12 inches of horizontal run.
inches OC
Jack rafter on-center spacing (16" or 24" OC).
Results & Graph
Hip / Valley Rafter Line Length
21 ft (252 in)
Common Rafter Line Length
15.65 ft
Jack Rafter Difference (@ 16" OC)
17.89 inches
Hip Rafter Plumb Pitch Angle
19.47 degrees

Hip / Valley Rafter Line Length

Graph 1 • Hip, Valley & Jack Rafters • Domain Architecture & Live Telemetry Maps Roof Span Width Feet, Roof Pitch Rise Per12, Rafter Spacing On Center In through Hip, Valley & Jack Rafters Formula.
INPUT PARAMETERS • Roof Span Width Fe: 28 ft • Roof Pitch Rise Pe: 6 in/12 • Rafter Spacing On : 16 inches OC ∑ F(x) Hip, Valley & Jack Rafters DESIGN OUTPUT 21 ft (252 in) Common Rafter Line Lengt: 15.65 ft Jack Rafter Difference (: 17.89 inches
Graph 2 • Hip / Valley Rafter Line Length Across Roof Span Width Feet Sweep (40% → 160%) Evaluates CommonFactor = √(12² + Pitch²)/12; HipFactor = √(17² + Pitch²)/12; J across 7 operating points (current input highlighted).
0 ft (25 18.48 ft (25 36.96 ft (25 8.40 11.20ft 12.60 16.80ft 16.80 22.40ft 21 28ft 25.20 33.60ft 29.40 39.20ft 33.60 44.80ft
Graph 3 • Joint Sensitivity: Roof Span Width Feet × Roof Pitch Rise Per12 Compares Hip / Valley Rafter Line Length when Roof Pitch Rise Per12 is shifted +25% (solid) vs. −25% (dashed).
0 ft (25 15.48 ft (25 30.95 ft (25 --- Roof Pitch Rise Per12 @ 75% 15.15 -30% 18.40 -15% 21.65 +0% 24.89 +15% 28.14 +30%
Summary: For a 28 ft span (14 ft run) at 6:12 pitch, Common Rafter is 15.65 ft, Hip/Valley Rafter is 21 ft (hip angle 19.47°), and Jack Rafter difference at 16" OC is 17.89".
Summary: For a 28 ft span (14 ft run) at 6:12 pitch, Common Rafter is 15.65 ft, Hip/Valley Rafter is 21 ft (hip angle 19.47°), and Jack Rafter difference at 16" OC is 17.89".
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Formula & Mathematical Methodology: Hip, Valley & Jack Rafters Formula

CommonFactor = 12² + Pitch²/12
HipFactor = 17² + Pitch²/12
JackDiff = (Spacingin / 12) × CommonFactor
CommonFactor = √(12² + Pitch²)/12; HipFactor = √(17² + Pitch²)/12; JackDiff = (Spacing_in / 12) × CommonFactor
  • roofSpanWidthFeet: Roof Span Width Feet (ft)
  • roofPitchRisePer12: Roof Pitch Rise Per12 (in/12)
  • rafterSpacingOnCenterIn: Rafter Spacing On Center In (inches OC)

Rounding: Engineering outputs round to 2–3 decimal places; discrete material bag/unit counts round up via ceiling.

Worked Example: Engineering Scenario: Hip, Valley & Jack Rafters

Compute Common, Hip/Valley, and Jack rafter lengths and compound cheek cut angles.

  1. Enter your system dimensions, electrical/RF ratings, or environmental conditions.
  2. Evaluate the governing equation: CommonFactor = √(12² + Pitch²)/12; HipFactor = √(17² + Pitch²)/12; JackDiff = (Spacing_in / 12) × CommonFactor.
  3. Inspect the primary design output, supporting allowances, and 3 SVG schematics.
Result: Computes Hip, Valley & Jack Rafters via CommonFactor = √(12² + Pitch²)/12; HipFactor = √(17² + Pitch²)/12; JackDiff = (Spacing_in / 12) × CommonFactor.

Frequently Asked Questions

How does the Hip & Valley Rafter Length (√(144+144+Rise²)/12), Jack Rafter Decrement & Backing Angle Calculator calculate results?

It evaluates CommonFactor = √(12² + Pitch²)/12; HipFactor = √(17² + Pitch²)/12; JackDiff = (Spacing_in / 12) × CommonFactor directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to solve backwards for a required dimension or rating?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input parameter.

Does this engineering calculator work offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

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Hip & Valley Rafter Length (√(144+144+Rise²)/12), Jack Rafter Decrement & Backing Angle Calculator: inputs, method, and how to read the result

Compute Common, Hip/Valley, and Jack rafter lengths and compound cheek cut angles.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Roof Span Width Feet: Total exterior building width (span = 2 × common run) in feet.
  • Roof Pitch Rise Per12: Roof pitch rise in inches per 12 inches of horizontal run.
  • Rafter Spacing On Center In: Jack rafter on-center spacing (16" or 24" OC).

What the calculation includes

With the default values shown, Hip / Valley Rafter Line Length is 21 ft (252 in). The calculation follows Hip, Valley & Jack Rafters Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Roof Span Width Feet from 28 ft to 31 ft changes Hip / Valley Rafter Line Length from 21 ft (252 in) to 23.25 ft (279 in). This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard NREL, IEEE, ASHRAE, and IRC design equations.
  • Verify final structural, electrical, and mechanical specifications against local building codes.

Scope: Global Engineering & Building Code Standard Check the assumptions and limitations against your situation before relying on the estimate.

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