Rafter Tools
Using the Law of Sines
c = ( a × sin( C ) ) ÷ sin( A)
c = Dormer Roof Rafter Length
C1 = 90° - Dormer Roof Pitch Angle
C2 = 90° - (Main Roof Pitch Angle - Dormer Roof Pitch Angle)
C = 90° - Dormer Roof Pitch Angle + (90° - (Main Roof Pitch Angle - Dormer Roof Pitch Angle))
C = C1 + C2
A = Main Roof Pitch Angle - Dormer Roof Pitch Angle
a = Dormer Roof Run
Dormer Roof Rafter Length = (Dormer Roof Run × sin(90° - Dormer Roof Pitch Angle + (90° - (Main Roof Pitch Angle - Dormer Roof Pitch Angle)))) ÷ sin(Main Roof Pitch Angle - Dormer Roof Pitch Angle )
or
Dormer Roof Rafter Length = (Dormer Roof Run × sin(C)) ÷ sin(A)
or
Dormer Altitude = sin(Dormer Roof Pitch Angle) × Dormer Run
Dormer Altitude Run = Dormer Altitude ÷ tan(Dormer Roof Pitch Angle)
Dormer Miter Cut Angle = Main Roof Pitch Angle - Dormer Roof Pitch Angle
Main Altitude Run = Dormer Altitude ÷ tan(Dormer Miter Cut Angle)
Dormer Rafter Length = Dormer Altitude Run + Main Altitude Run
Main Intercept Run = (Dormer Rafter Length × cos( Dormer Roof Pitch Angle)) - Dormer Run
An example of the calculated results that you can email yourself in the Rafter Tools app
Rafter Tools -- Dormer Shed Roof Calculations
| Main Rafter Slope Angle | 33.69007° | Main Rafter Pitch | 8 in\12in | Main Rafter HAP | 7 3/4''in | Main Roof Sheathing Material Thickness | 1/2''in | Main Roof Rafter Material Depth | 9 1/2''in | Main Roof Rafter Plumb Height | 11 7/16''in | Main Run | 28 1/4''in | Main Intercept Run | 32 7/16''in | Dormer Rafter Slope Angle | 14.03624° | Dormer Rafter Pitch | 3 in\12in | Dormer Rafter HAP | 8 7/16''in | Dormer Run | 54 ''in | Dormer Roof Rafter Material Depth | 9 1/2''in | Dormer Roof Rafter Plumb Height | 9 13/16''in | Dormer Sleeper Material Thickness | 1 1/2''in | Dormer & Main Roof Plate Line Difference | 0 | Dormer Rafter Length | 84 3/4''in | Dormer Sleeper Bevel Length | 4 7/16''in | Dormer Miter Cut Angle | 19.65382° | Dormer Rafter Miter Cut Length | 28 1/4''in | Dormer Intercept Run | 82 1/4''in | Main Roof Slope Intercept Length | 29 3/4''in | Dormer Rafter Length To Main Roof Sheathing Without Sleeper | 89 1/4''in |
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