Hip-Valley Roof Ratios Angle Formulas
Common Rafter Slope Angle SS or S
• SS = arctan (Rise ÷ Run)
• SS = arccos (tan P2 x tan DD)
• SS = arccos (tan DD ÷ tan 90 - P2)
• SS = arccos (cos R1 x cos C5)
• SS = arcsin (sin R1 ÷ cos P2)
• SS = arcsin (sin R1 ÷ sin 90 - P2)
• SS = arctan (tan R1 ÷ sin DD)
• SS = arcsin (sin C5 ÷ cos DD)
• SS = arctan (tan C5 ÷ sin P2)
• SS = arctan (tan C5 ÷ cos 90 - P2)

• SS = arccos (tan Jack Rafter Side Cut Angle x tan Plan Angle)
• SS = arccos (tan Plan Angle ÷ tan Sheathing Angle)
• SS = arccos (cos Hip-Valley Pitch Angle x cos Backing Angle)
• SS = arcsin (sin Hip-Valley Pitch Angle ÷ cos Jack Rafter Side Cut Angle)
• SS = arcsin (sin Hip-Valley Pitch Angle ÷ sin Sheathing Angle)
• SS = arctan (tan Hip-Valley Pitch Angle ÷ sin Plan Angle)
• SS = arcsin (sin Backing Angle ÷ cos Plan Angle)
• SS = arctan (tan Backing Angle ÷ sin Jack Rafter Side Cut Angle)
• SS = arctan (tan Backing Angle ÷ cos Sheathing 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.