Unequal Pitch Roof Trigonometry Calculating unequal pitched roofs is easy if you know what trigonometry functions to use. The formulas below use the law of sines to calculate the unknown length or angle. Known Variables: Major Pitch Angle & Minor Pitch Angle & Span & Plate Line Difference Calculate Major & Minor Runs & Theoretical Plate Line Span Theoretical Span = Span  (Plate Line Difference ÷ tan(Minor Pitch Angle)) Plate Line Difference Run = Span  Theoretical Span Major Run = ((Theoretical Span × sin(Minor Pitch Angle)) ÷ sin (180  Major Pitch Angle  Minor Pitch Angle)) × cos( Major Pitch Angle ) Theoretical Minor Run = ((Theoretical Span * sin(Major Pitch Angle)) ÷ sin (180  Major Pitch Angle  Minor Pitch Angle)) × cos( Minor Pitch Angle ) Minor Run = Theoretical Minor Run + Plate Line Difference Run Major Rafter = Major Run ÷ cos (Major Pitch Angle) Theoretical Minor Rafter = Theoretical Minor Run ÷ cos (Minor Pitch Angle) Plate Line Difference Minor Rafter = Plate Line Difference Run ÷ cos (Minor Pitch Angle) Minor Rafter = Minor Run ÷ cos (Minor Pitch Angle) Roof Rise = Major Run × tan (Major Pitch Angle) Total Minor Roof Rise = Minor Run × tan (Minor Pitch Angle) Law Of Sines C = 180°  (A + B) a = ( c × sin( A) ) ÷ sin( C) a = ( b × sin( A ) ) ÷ sin( B) a = ( b ÷ sin( B ) ) × sin( A) b = ( c × sin( B ) ) ÷ sin( C) b = ( a × sin( B ) ) ÷ sin( A) b = ( a ÷ sin( A ) ) × sin( B) h = b × sin( A ) h = a × sin( B ) c = ( a × sin( C ) ) ÷ sin( A) c = ( b × sin( C ) ) ÷ sin( B)
RFI  structural  framing  online tools  company  site map
safety  building resource links  build it green  photo gallery  Octagon  crown molding angles  home
WindsorOne Protected Trim
 SBE Builders 5305 Laguna Ct. Discovery Bay, California 94505 (925) 6346022 • Fax: (925) 6346022
Commercial & Residential Framing Contractor American Carpenter and Builder California Licensed General Building Contractor CA LIC.# 546126 
Roof Framing Geometry

Rafter Tools for Android
With Quad Tetrahedra Analytic Algorithm Technology.
Helping apprentice carpenters on their journey to becoming master carpenters with Certification in roof framing.
Crown Molding Tools
crownmoldingtools.com
Canadian & American Geometric Roof Framing Development
using a Steel Framing Square
Geometric Roof Framing Development for Irregular Hip Roof Calculations
using a Steel Framing Square
Geometric Development of Tetrahedron
using a Steel Framing Square
Hip Rafter Backing Bevel Angles from 1565 to 2013