HawkinDale Formula
• R1 = arctan (tan SS x sin DD)

Hip-Valley Roof Ratios Angle Formulas
• R1 = arccos (cos SS ÷ cos C5)
• R1 = arctan (tan SS x sin DD)
• R1 = arcsin (sin SS x cos P2)
• R1 = arcsin (sin SS x sin 90 - P2)
• R1 = arccos (sin P2 ÷ cos DD)
• R1 = arccos (cos 90 - P2 ÷ cos DD)
• R1 = arcsin (tan DD x tan C5)
• R1 = arctan (sin C5 ÷ tan P2)
• R1 = arctan (sin C5 x tan 90 - P2)

• R1 = arccos (cos Common Rafter Pitch Angle ÷ cos Backing Angle)
• R1 = arctan (tan Common Rafter Pitch Angle x sin Plan Angle)
• R1 = arcsin (sin Common Rafter Pitch Angle x cos Jack Rafter Side Cut Angle)
• R1 = arcsin (sin Common Rafter Pitch Angle x sin Sheathing Angle)
• R1 = arccos (sin Jack Rafter Side Cut Angle ÷ cos Plan Angle)
• R1 = arccos (cos Sheathing Angle ÷ cos Plan Angle)
• R1 = arcsin (tan Plan Angle x tan Backing Angle)
• R1 = arctan (sin Backing Angle ÷ tan Jack Rafter Side Cut Angle)
• R1 = arctan (sin Backing Angle x tan Sheathing Angle)
• Hip Rafter Slope Angle = arctan( tan( Pitch Angle ) * sin( Plan Angle ))

The Hip-Valley Roof Ratios Angle Formulas were developed by Joe Bartok.

The Timber Framing Hawkindale Angle Formulas were developed by Rees Hawkins Acheson from the Martindale Hip and Valley Roof Angles and Hawkindale angle drawings by Ed Levin of the Timber Framers Guild.

The Hawkindale angles were based on the book by Frank L. Martindale "Bevel Angles for Three Dimensional Connections" 1948 that was based on the book "Hip and Valley Design" by H. L. McKibben and L. E. Gray published in 1912.