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Dihedral Angle Calculator, determine the compound angle formed by the intersection of two intersecting planes

The purpose of this page is to help you calculate the saw blade angle, or joint angle of the dihedral. A dihedral in geometric terms is the line formed where two planes (or climbing wall panels) intersect. This is a common situation when building climbing walls. Often, two panels will intersect at arbitrary angles. Often it is possible to take this measurement directly. However this is not always possible. This is an online calculator for determining the compound angle, or the dihedral angle where two panels meet. From this, the joint angles for the plywood edge and framing members can be determined.

Dihedral as a Climbing Term vs a Geometric Dihedral

This bears explanation because the term as used on this page is the geometric dihedral, yet the audience are climbers. So let me explain the difference...  In the sport of climbing, a dihedral is a rock formation that is nearly vertical and forming a fairly sharp angle at the "dihedral" end. The meaning of dihedral when used as a geometric term is the line or vector that is formed along the intersection of two planes. In the context of building an indoor climbing wall, it is the line where the two climbing surfaces intersect. The intersection is the dihedral. The angle between the two panels is the dihedral angle.

Determine the dihedral angle so you know the miter angle setting for the saw blade. The calculator will give you the dihedral and joint angle for situations where you cannot measure it directly. When your walls are inclined, the dihedral angle is not the same angle as the angle on the horizontal plane. Adjusting your joint by this calculation will give you an exact and solid joint. Be sure to verify all angles using scrap wood before making your cuts.

Why Calculate Dihedral Angle

When building a climbing wall, it is useful to have the angle which the two climbing faces meet. The builder may not be able to take a direct measurement prior to building, and as a result may need to know this angle during the design phase.

How to find the Dihedral Angle

This online dihedral angle calculator gives you the angle between two planes. The planes, or panels can be elevated, inclined, rotated, or an any position or orientation.

How to Use the Dihedral Angle Calculator

The calculator is populated with the example's numbers. Just change the numbers with your measurements and click "Calculate Angle".

Coordinate Locations DescriptionsX, Y, Z Coordinates Dihedral Angle Illustration
Bottom Joint
X: 
Y:
Z:

Example: Fit a wall panel into the opening. Determine the correct angles for the joints.
Shown below are the coordinates and resulting angles for the left joint (highlighted in blue).

Dihedral Angle Example

Front View. Coordinates for two points on the top and bottom left joint, and one other coordinate point on each panel.

Dihedral Angle Example

Rear View. The angle on the horizontal plane is 45 degrees, but the dihedral angle which the two panels meet is 41 degrees.

The left dihedral angle formed by the panel on the left and the triangular opening can be calculated by inputting the coordinates as shown. Notice that the angle at the base (the floor or horizontal plane) is 45 degrees. However, due to the slanting of the panels, the dihedral angle is not equal to the angle of the horizontal plane. The new triangular panel will form a joint with the panel on the left at an angle of 41 degrees along the dihedral. It may not seem like a lot of difference, but it's definitely enough to cause a loose joint.

Note: Verify all angles using scrap wood before cutting lumber or plywood.

Top Joint
X: 
Y:
Z:
Left End
X: 
Y:
Z:
Right End
X: 
Y:
Z:
Dihedral Angle:
Joint Angle
139
41
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