Hopper Miter Angle and Saw Blade Bevel Angle Settings Development
Hopper angles are the same angles that are use for cutting roof sheathing.
The hopper miter angle is the same as the jack rafter side cut angle and the
hopper saw blade bevel angle is the same as the hip rafter backing angle.
The crown spring angle is measured on a vertical plane. The hopper
slope angle is measured on a horizontal plane.
Roof Pitch Angle = Hopper Slope Angle
Use any of these formulas to find the Hopper Miter Angle
Hopper Miter Angle = arccos( sin ( Plan Angle ) ÷ cos ( Hip Rafter
Backing Angle ))
Hopper Miter Angle = arccos( sin ( Hip Rafter Angle ) ÷ sin ( Roof
Pitch Angle ))
Hopper Miter Angle = arcsin ( cos ( Plan Angle ) × cos ( Hip Rafter
Angle ))
Hopper Miter Angle = arcsin ( tan ( Hip Rafter Backing Angle ) ÷ tan
( Roof Pitch Angle ))
Hopper Miter Angle = arctan( cos ( Roof Pitch Angle ) ÷ tan ( Plan
Angle ))
Hopper Miter Angle = arctan( sin ( Hip Rafter Backing Angle ) ÷ tan
( Hip Rafter Angle ))
Use any of these formulas to find the Hopper Saw Blade Bevel Angle
Hopper Saw Blade Bevel Angle = arccos( sin ( Plan Angle ) ÷ cos ( Jack
Rafter Side Cut Angle ))
Hopper Saw Blade Bevel Angle = arccos( cos ( Roof Pitch Angle ) ÷ cos
( Hip Rafter Angle ))
Hopper Saw Blade Bevel Angle = arcsin ( sin ( Roof Pitch Angle ) × cos
( Plan Angle ))
Hopper Saw Blade Bevel Angle = arcsin ( tan ( Jack Rafter Side Cut Angle )
× tan ( Hip Rafter Angle ))
Hopper Saw Blade Bevel Angle = arctan( tan ( Roof Pitch Angle ) × sin
( Jack Rafter Side Cut Angle ))
Hopper Saw Blade Bevel Angle = arctan( sin ( Hip Rafter Angle ) ÷ tan
( Plan Angle ))
Hopper Miter Angle = arctan (cos(Roof Pitch Angle) ÷ tan (Plan Angle))
Hopper Saw Blade Bevel Angle = arctan( sin ( Hip Rafter Angle ) ÷ tan
( Plan Angle ))
example:
Roof Pitch Angle = 38°
Wall Angle = 90°
Plan Angle = 45°
Hip Rafter Angle = arctan( tan ( 38° ) × sin ( 45 )) = 28.91856°
Hopper Miter Angle = arctan (cos( 38° ) ÷ tan( 45° )) = 38.23849°
Hopper Saw Blade Bevel Angle = arctan( sin( 28.91856° ) ÷ tan(
45° )) = 25.80683°
or
Hopper Miter Angle = arctan (cos(Roof Pitch Angle) ÷ tan (Plan Angle))
Hopper Saw Blade Bevel Angle = arccos( sin ( Plan Angle ) ÷ cos ( Hopper
Miter Angle ))
Hopper Miter Angle = arctan (cos( 38° ) ÷ tan( 45° )) = 38.23849°
Hopper Saw Blade Bevel Angle = arccos( sin( 45° ) ÷ cos( 38.23849°
)) = 25.80683°
Polygon table with hopper base and IPE decking table top. All of the lumber used for this table were left overs from different jobs.
Martindale's Bin and Hopper Angles Case Study 3
Bevel angles for three dimensional connections: Tapered bin, hopper & tower corner angles : hip and valley roof framing connections : analytic proof of ... of hip & valley bevel connection angles
RFI  structural  framing  online tools  company  site map
safety  building resource links  build it green  photo gallery  Octagon  crown molding angles  home
WindsorOne Protected Trim
 SBE Builders 5305 Laguna Ct. Discovery Bay, California 94505 (925) 6346022 • Fax: (925) 6346022
Commercial & Residential Framing Contractor American Carpenter and Builder California Licensed General Building Contractor CA LIC.# 546126 
Roof Framing Geometry

Rafter Tools for Android
With Quad Tetrahedra Analytic Algorithm Technology.
Helping apprentice carpenters on their journey to becoming master carpenters with Certification in roof framing.
Crown Molding Tools
crownmoldingtools.com
Canadian & American Geometric Roof Framing Development
using a Steel Framing Square
Geometric Roof Framing Development for Irregular Hip Roof Calculations
using a Steel Framing Square
Geometric Development of Tetrahedron
using a Steel Framing Square
Hip Rafter Backing Bevel Angles from 1565 to 2013