SBE Builders

Strong Built Establishments Builders

SBE Builders is a commercial and residential framing contractor located in Discovery Bay California. Dedicated to the art of Carpentery & Roof Framing. We are the professionals for the future of the craft of carpentry.

This Eyebrow Roof Dormer calculator will return roof framing trigonometry & geometry details for:

  1. Eyebrow Roof Dormer Semi Major Axis of the Elliptical Valley Footprint
  2. Eyebrow Roof Dormer Plan View Run of the Ellipse from the intersection of the eyebrow roof and main roof.
  3. Total Arc Length of Eyebrow Roof Dormer
  4. Arc Angle of Purlin Rafter Spacing
  5. Cord Length of Purlin Rafter Spacing
  6. Ellipse layout points on Main Roof Surface
  7. Purlin Rafters cut perpendicular to Roof Surface
  8. Purlin Rafter Slope Angle
  9. Purlin Rafter Miter Angle
  10. Purlin Rafter Saw Blade Bevel Angle
  11. Eyebrow Roof Dormer Plan View Rafter Lengths
  12. X & Y Points for Elliptical Ploting of the Ellipse on the Main Roof Surface
  13. Real Roof Surface plotting points for the plywood roof sheathing
  14. Ellipse Valley Sleeper Offset
  15. Purlin Rafter Deduction for Ellipse Valley Sleeper Offset

Eyebrow Roof Dormer Framing Calculator

Eyebrow Dormer Roof Details
    Main Roof Pitch
    Eyebrow Dormer Pitch

Purlin Rafter O.C. Spacing
Entered in Inches

    Eyebrow Dormer Height
Entered in Inches
    Eyebrow Dormer Width
Entered in Inches

show results in feet & inches

results are show below in the IFrame window

Eyebrow Roof Dormer

Eyebrow Roof Dormer Roof Framing

Eyebrow Roof Dormer Framing Math & Trigonometry

Ellipse Formulas for Eyebrow Roof Design

Intersecting Slope Angle = arctan((Roof Pitch - Dormer Pitch ) ÷ 12)
Semi Minor Axis = Radius
Roof Surface Semi Major Axis = ( Radius ÷ tan( Intersecting Slope Angle ) ) ÷ cos( Roof Pitch Angle )
Plan View Semi Major Axis = Radius ÷ tan( Intersecting Slope Angle )
Elevation View Semi Major Axis = ( Radius ÷ tan( Intersecting Slope Angle ) ) * tan( Roof Pitch Angle )

Arc Angle Of Spacing in Radians = spacing  radius (This gives you the arc angle in radians)
Degree to Radians = 3.141593  180   = 0.017453
Radians to Degrees = 180  3.141593  = 57.29578
Arc Angle of Spacing in Degrees = (spacing  radius ) * 57.29578 = Arc Angle in Degrees

Purlin Face Cut Perpendicular to Roof Surface
Purlin Pitch Angle = Main Roof Pitch Angle - Eyebrow Dormer Roof Pitch Angle
Saw Blade Miter  Angle = arctan (cos(Purlin Pitch Angle)  tan(Roof Pitch Angle))
Saw Blade Bevel Angle = arcsin (cos(Roof Pitch Angle) * sin(Purlin Pitch Angle))

Download Eyebrow Roof Dormer Framing Drawing in DXF format
Eyebrow Roof Dormer Framing.dxf -- auto generated DXF CAD file of Eyebrow Roof Dormer Framing drawing each time script is run
Eyebrow Dormer Roof DXF File


You can bevel the ellipse valley sleeper material or slide the ellipse valley sleeper material down hill by the ellipse valley sleeper offset dimension.
When you offset the ellipse valley sleeper, the ellipse dimensions stay the same for both ellipses.
In the image below you can see the direction of the ellipse valley sleeper bevel is a constant dimension between the two ellipses.


Eyebrow Ellipse Offset



Down load the Eyebrow Roof Dormer Cut Out Pattern HERE for a paper model of the eyebrow roof geometry.


Eyebrow Roof Cut Out Pattern


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SBE Builders
SBE Builders
5305 Laguna Ct.
Discovery Bay, California 94505
(925) 634-6022 • Fax: (925) 634-6022
Commercial & Residential Framing Contractor
American Carpenter and Builder
California Licensed General Building Contractor
CA LIC.#  546126

Roof Framing Geometry

  • Roof framing geometry is empirical-type knowledge.
  • Information gained by means of observation, experience, or experiment.
  • From ground Line 0: Z1, Z2, Z3 etc...
  • To Roof Axis 0: A1, A2, A3 etc...
  • To the bring back line 0 for scribing: B1, B2, B3 etc...

Roof Framing Geometry Blog

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Stair Tangent

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This Is Carpentry

We're a member of the Timber Framers Guild

Timber Framers Guild

American College of the Building Arts, carpentry and timber framing programs.

American College of the Building Arts

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