Crown Molding Tools
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Upside down and backwards in a miter box or compound miter saw has been used
for the last 200+ years by the majority of carpenters to cut crown molding miter
and bevel angles. Right sideup and backwards for rake crown molding cuts were
developed long before our time, but even today there's still confusion about the
correct crown miter and bevel angles when cutting rake crown molding laying flat
in the miter box or compound miter saw. By using plane geometry for developing
rake crown molding profiles you can determine the correct miter and bevel angles
for rake crown molding.
Trigonometric Relationships between Tetrahedron Angles by Joe Bartok
Joe Bartok's Trigonometric Relationships between Tetrahedron Angles web page is th
significant treatise on roof framing angles in the last 100 years. If your a roof framer print o
Trigonometric Relationships between Tetrahedron Angles web page and study the trigonome
relationships between each of the triangles. If your an interior trim carpenter, then just use
angle formulas below.
Trigonometric Crown Angle Formulas for Horizontal Plane Crown Molding Angles
Crown Miter Angle = arctan (sin( Spring Angle) ÷ tan ( Wall Corner Angle ÷ 2 ))
Crown Miter Angle = arctan (sin( 38°) ÷ tan( 45°)) = 31.62°
Crown Bevel Angle = arcsin (cos( Spring Angle ) * cos( Wall Corner Angle ÷ 2 ))
Crown Bevel Angle = arcsin (cos( 38°) * cos( 45°)) = 33.86°
or you can think of the wall angle as the miter bisect angle
Crown Miter Angle = arctan (sin( Spring Angle) ÷ tan ( Wall Miter Bisect Angle ))
Crown Miter Angle = arctan (sin( 38°) ÷ tan( 45°)) = 31.62°
Crown Bevel Angle = arcsin (cos( Spring Angle ) * cos( Wall Miter Bisect Angle))
Crown Bevel Angle = arcsin (cos( 38°) * cos( 45°)) = 33.86°
or you use the crown slope angle instead of the crown spring angle for horizontal plane crow
angles
Crown Miter Angle = arctan (cos(Crown Slope Angle) * tan( Wall Miter Bisect Angle ))
Crown Miter Angle = arctan (cos( 52°) * tan( 45°)) = 31.62°
Crown Bevel Angle = arcsin (sin( Crown Slope Angle ) * sin( Wall Miter Bisect Angle))
Crown Bevel Angle = arcsin (sin( 52° ) * sin( 45°)) = 33.86°
Trigonometric Crown Angle Formulas for Vertical Plane Crown Molding Angles
(cathedral/vaulted ceilings/rake gables)
Crown Miter Angle = arctan (cos( Spring Angle) ÷ tan((180° - (Roof Pitch Angle * 2)) ÷ 2 )
Crown Miter Angle = arctan (cos( 38°) ÷ tan((180° - (33.69° * 2)) ÷ 2)) = 27.71°
Crown Miter Angle = arctan (cos( 38°) ÷ tan(56.31) = 27.71°
Crown Bevel Angle = arcsin (sin( Spring Angle ) * cos((180° - (Roof Pitch Angle * 2)) ÷ 2))
Crown Bevel Angle = arcsin (sin( 38°) * cos( 56.31°)) = 19.97°
Development of Tetrahedron Geometry
based on Joe Bartok's Tetrahedron Developmental Geometry
Development of Tetrahedron Geometry
Development of Tetrahedron for Crown Molding Geometry Using Spring Angle and Wall Angl
Development of Tetrahedron for Crown Molding Geometry Using Slope Angle and Corner Pla
Development of Tetrahedron for Crown Rake Molding Geometry
Crown Moulding Miter Angle and Bevel Angle Settings Calculators
Crown Spring Angle = 52°
Crown Spring Angle = 45°
Crown Spring Angle = 38°
Wall Angle Settings
Rake Crown Spring Angle = 38°
Rake to Horizontal Crown Spring Angle = 38°
Polygon 2 Cord Exterior Rake Gable Crown Molding Miter Angle and Bevel Angle Settings
Polygon 2 Cord Interior Rake Gable Crown Molding Miter Angle and Bevel Angle Settings
Polygon Crown Molding Angles Development & Calculator
Octagon Roof Exterior Crown Molding Angles Development Calculators
Octagon Roof Interior Crown Molding Angles Development Calculators
Corner A Crown Molding Calculator
Corner B Crown Molding Calculator
Corner C Crown Molding Calculator
Corner D Crown Molding Calculator
Polygon Crown Molding Miter Angles and Bevel Angles
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Crown Molding Tools
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Carpenters Of Steel
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