Irregular Roof Dimensions
Dimensions are in decimal feet to the theoretical framing points

 8/12 Common Rafter Pitch Angle = arctan (8/12) = 33.690068° 14/12 Common Rafter Pitch Angle = arctan (14/12) = 49.398705° 8/12 Run = 37 ÷ 2 =18.5 Rise = 18.5 × tan 33.690068° = 12.333333

 Plan Angles at 90° Eave between 8/12 and 14/12 Commons arctan (14/8) = 60.255119° arctan (8/14) = 29.744881° 14/12 Run = 18.5 × sin 29.744881° ÷ sin 60.255119° = 10.571428 Hip Pitch Angle = arctan (8 × sin 60.255119° ÷ 12) = 30.063493° Plan Angles at 135° Eave between 14/12 and 915/16/12 Commons arctan (10.571428/10.5) = 45.194221° 135° - 45.194221° = 89.805779° Hip Pitch Angle = arctan (14 × sin 45.194221° ÷ 12) = 39.616244° Common Pitch Angle = arctan (tan 39.616244° ÷ sin 89.805779°) = 39.616406° Common Pitch = 12 × tan 39.616406° = 9.933052 = approx. 915/16/12 Plan Angles at 135° Eave between 915/16/12 and 8/12 Commons arctan [sin 135° ÷ ( tan 39.616406° / tan 33.690068° + cos 135°)] = 52.913194° 135° - 52.913194° = 82.086806° Hip Pitch Angle = arctan (tan 39.616406° × sin 52.913194° = 33.437522°

Hip-Valley Roof Framing Calculator Entries and Returns

 90° Eave between 8/12 and 14/12 Commons Main Span Pitch Angle = 33.690068° Adjacent Span Pitch Angle = 49.398705° Total Deck Angle = 90° Main Span Dimension = 37 ft. Hip Pitch Angle = 30.06349° (615/16/12) Hip Rafter Run = 21.30740' = 21' - 3 11/16" Hip Rafter Length = 24.61943' = 24' - 7 7/16" Sheathing Angle on 8/12 Side = 64.57091° Jack Diff. in Length (16" spacing) = 2.80432' = 2' - 9 5/8" Sheathing Angle on 14/12 Side = 41.28481° Jack Diff. in Length (16" spacing) = 1.17074' = 1' - 2 1/16" 135° Eave between 14/12 and 915/16/12 Commons Main Span Pitch Angle = 49.398705° Adjacent Span Pitch Angle = 39.616406° Total Deck Angle = 135° Main Span Dimension = 2 × 10.571428 ft. = 21.142856 ft. Hip Pitch Angle = 39.61624° (915/16/12) Hip Rafter Run = 14.89983' = 14' - 10 13/16" Hip Rafter Length = 19.34208' = 19' - 4 1/8" Sheathing Angle on 14/12 Side = 57.12161° Jack Diff. in Length (16" spacing) = 2.06272' = 2' - 0 3/4" Sheathing Angle on 915/16/12 Side = 89.85038° * Jack Diff. in Length (16" spacing) = 2' - 3 1/2" (Sheathing Angle near 90° , use dimension for 59.78700° below) 135° Eave between 915/16/12 and 8/12 Commons Main Span Pitch Angle = 33.690068° Adjacent Span Pitch Angle = 39.616406° Total Deck Angle = 135° Main Span Dimension = 37 ft. Hip Pitch Angle = 33.43752° (715/16/12) Hip Rafter Run = 18.67785' = 18' - 8 1/8" Hip Rafter Length = 22.38243' = 22' - 4 9/16" Sheathing Angle on 8/12 Side = 83.40295° Jack Diff. in Length (16" spacing) = 11.52886' = 11' - 6 3/8" Sheathing Angle on 915/16/12 Side = 59.78700° * Jack Diff. in Length (16" spacing) = 2.28970' = 2' - 3 1/2"

Hip Rafter Sections detailing Backing Angles and Hip Drops