Hip/Valley Rafter Backing Angle Chart in decimal inches

Eave Angle = 135°
Plan Angle = 67.5°
Pitch Angle = arctan ( Pitch ÷ 12)
Hip Pitch Angle = arctan( tan (Pitch Angle) * sin ( Plan Angle))
Hip Backing Angle = arctan ( sin ( Hip Pitch Angle) ÷ tan ( Plan Angle) )
Hip Backing Angle Rise = ( Material Width * .5 ) * tan ( Hip Backing Angle) ) or Valley Trough Depth
Plan Angle Unit Rise = tan ( Plan Angle )
Hip Unit Rise Run = 12 ÷ sin ( Plan Angle )
Unit Hip Drop = Pitch ÷ ( Hip Unit Rise Run * (Plan Angle Unit Rise * 2 )
Hip Drop Adjustment = ( Material Width * .5 ) * Unit Hip Drop
Plumb Backing Angle = tan (Hip Pitch Angle) ÷ tan (Plan Angle)
Plumb Backing Angle Rise = Backing Angle Rise ÷ cos Hip Pitch Angle
Pitch Pitch Angle Hip Angle Hip Backing Angle Hip Plumb Backing Angle 2x
rise  drop  plumb		 3x
rise  drop  plumb		 3 1/8
rise  drop  plumb		 4x
rise  drop  plumb		 5 1/8
rise  drop  plumb		 6x
rise  drop  plumb
3 14.04° 13.01° 5.33° 5.46° 0.07 0.07 0.07 0.14 0.14 0.14 0.15 0.15 0.15 0.16 0.17 0.17 0.24 0.25 0.25 0.26 0.26 0.26
4 18.43° 17.12° 6.95° 7.27° 0.09 0.10 0.10 0.18 0.19 0.19 0.19 0.20 0.20 0.21 0.22 0.22 0.31 0.33 0.33 0.34 0.35 0.35
5 22.62° 21.05° 8.46° 9.06° 0.11 0.12 0.12 0.22 0.24 0.24 0.23 0.25 0.25 0.26 0.28 0.28 0.38 0.41 0.41 0.41 0.44 0.44
6 26.57° 24.79° 9.85° 10.83° 0.13 0.14 0.14 0.26 0.29 0.29 0.27 0.30 0.30 0.30 0.33 0.33 0.45 0.49 0.49 0.48 0.53 0.53
7 30.26° 28.32° 11.12° 12.58° 0.15 0.17 0.17 0.29 0.33 0.33 0.31 0.35 0.35 0.34 0.39 0.39 0.50 0.57 0.57 0.54 0.61 0.61
8 33.69° 31.63° 12.26° 14.31° 0.16 0.19 0.19 0.33 0.38 0.38 0.34 0.40 0.40 0.38 0.45 0.45 0.56 0.65 0.65 0.60 0.70 0.70
9 36.87° 34.72° 13.27° 16.01° 0.18 0.22 0.22 0.35 0.43 0.43 0.37 0.45 0.45 0.41 0.50 0.50 0.60 0.74 0.74 0.65 0.79 0.79
10 39.81° 37.59° 14.18° 17.69° 0.19 0.24 0.24 0.38 0.48 0.48 0.39 0.50 0.50 0.44 0.56 0.56 0.65 0.82 0.82 0.69 0.88 0.88
11 42.51° 40.26° 14.99° 19.33° 0.20 0.26 0.26 0.40 0.53 0.53 0.42 0.55 0.55 0.47 0.61 0.61 0.69 0.90 0.90 0.74 0.96 0.96
12 45.00° 42.73° 15.70° 20.94° 0.21 0.29 0.29 0.42 0.57 0.57 0.44 0.60 0.60 0.49 0.67 0.67 0.72 0.98 0.98 0.77 1.05 1.05
13 47.29° 45.02° 16.33° 22.52° 0.22 0.31 0.31 0.44 0.62 0.62 0.46 0.65 0.65 0.51 0.73 0.73 0.75 1.06 1.06 0.81 1.14 1.14
14 49.40° 47.15° 16.89° 24.06° 0.23 0.33 0.33 0.46 0.67 0.67 0.47 0.70 0.70 0.53 0.78 0.78 0.78 1.14 1.14 0.84 1.23 1.23
15 51.34° 49.11° 17.39° 25.56° 0.23 0.36 0.36 0.47 0.72 0.72 0.49 0.75 0.75 0.55 0.84 0.84 0.80 1.23 1.23 0.86 1.32 1.32
16 53.13° 50.93° 17.83° 27.03° 0.24 0.38 0.38 0.48 0.77 0.77 0.50 0.80 0.80 0.56 0.89 0.89 0.82 1.31 1.31 0.88 1.40 1.40

Hip/Valley Rafter Backing Angle Chart in feet & inches

Pitch Pitch Angle Hip Angle Hip Backing Angle Hip Plumb Backing Angle 2x
rise  drop  plumb		 3x
rise  drop  plumb		 3 1/8
rise  drop  plumb		 4x
rise  drop  plumb		 5 1/8
rise  drop  plumb		 6x
rise  drop  plumb
3 14.04° 13.01° 5.33° 5.46° 1/8 1/8 1/8 3/16 3/16 3/16 3/16 3/16 3/16 3/16 3/16 3/16 1/4 1/4 1/4 5/16 5/16 5/16
4 18.43° 17.12° 6.95° 7.27° 1/8 1/8 1/8 3/16 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 5/16 3/8 3/8 3/8 3/8 3/8
5 22.62° 21.05° 8.46° 9.06° 1/8 1/8 1/8 1/4 1/4 1/4 1/4 1/4 1/4 5/16 5/16 5/16 7/16 7/16 7/16 7/16 1/2 1/2
6 26.57° 24.79° 9.85° 10.83° 3/16 3/16 3/16 5/16 5/16 5/16 5/16 5/16 5/16 5/16 3/8 3/8 1/2 1/2 1/2 1/2 9/16 9/16
7 30.26° 28.32° 11.12° 12.58° 3/16 3/16 3/16 5/16 3/8 3/8 5/16 3/8 3/8 3/8 7/16 7/16 9/16 5/8 5/8 9/16 5/8 5/8
8 33.69° 31.63° 12.26° 14.31° 3/16 1/4 1/4 3/8 7/16 7/16 3/8 7/16 7/16 7/16 1/2 1/2 9/16 11/16 11/16 5/8 3/4 3/4
9 36.87° 34.72° 13.27° 16.01° 3/16 1/4 1/4 3/8 7/16 7/16 3/8 1/2 1/2 7/16 9/16 9/16 5/8 3/4 3/4 11/16 13/16 13/16
10 39.81° 37.59° 14.18° 17.69° 1/4 1/4 1/4 7/16 1/2 1/2 7/16 1/2 1/2 1/2 9/16 9/16 11/16 7/8 7/8 3/4 15/16 15/16
11 42.51° 40.26° 14.99° 19.33° 1/4 5/16 5/16 7/16 9/16 9/16 7/16 9/16 9/16 1/2 5/8 5/8 11/16 15/16 15/16 3/4 15/16 15/16
12 45.00° 42.73° 15.70° 20.94° 1/4 5/16 5/16 7/16 5/8 5/8 1/2 5/8 5/8 1/2 11/16 11/16 3/4 1 1 13/16 1 1/16 1 1/16
13 47.29° 45.02° 16.33° 22.52° 1/4 5/16 5/16 1/2 5/8 5/8 1/2 11/16 11/16 9/16 3/4 3/4 13/16 1 1/16 1 1/16 13/16 1 3/16 1 3/16
14 49.40° 47.15° 16.89° 24.06° 1/4 3/8 3/8 1/2 11/16 11/16 1/2 3/4 3/4 9/16 13/16 13/16 13/16 1 3/16 1 3/16 7/8 1 1/4 1 1/4
15 51.34° 49.11° 17.39° 25.56° 1/4 3/8 3/8 1/2 3/4 3/4 1/2 3/4 3/4 9/16 7/8 7/8 13/16 1 1/4 1 1/4 7/8 1 3/8 1 3/8
16 53.13° 50.93° 17.83° 27.03° 1/4 7/16 7/16 1/2 13/16 13/16 9/16 13/16 13/16 5/8 15/16 15/16 7/8 1 5/16 1 5/16 15/16 1 7/16 1 7/16

Revolution of the Cutting Plane by Joe Bartok
Hip Drop, Mark & Back Bevel Angle by Joe Fusco
Hip and Valley Backing Angles