Angle Cut Calculator

The Angle Cut Calculator finds miter angles and plank offsets for knee bracing in framing and woodworking. Enter plank thickness plus two outer leg measurements to get cut angles $\alpha$ and $\beta$, outer diagonal length $C$, and marking offsets $C_a$ and $C_b$.

Knee bracing geometry

A knee brace forms a right triangle between a post and beam. The outer diagonal length is:

$$C = \sqrt{A^2 + B^2}$$

Cut angles at each end are:

$$\alpha = \arccos\left(\frac{A}{C}\right), \quad \beta = 90° - \alpha$$

Marking offsets along the plank ends account for material thickness $t$:

$$C_a = \frac{t}{\tan(\alpha)}, \quad C_b = \frac{t}{\tan(\beta)}$$

Related tools: Miter Angle Calculator and Triangle Calculator.

Frequently Asked Questions

What is knee bracing?

Knee bracing is a diagonal member between a vertical post and horizontal beam. It resists racking and adds stiffness to post-and-beam frames, sheds, and open structures.

Why do cut angles depend on plank thickness?

Angled cuts are made on the edge of the board. Thickness shifts where the cut plane meets the face, so offset distances $C_a$ and $C_b$ must be marked before cutting.

Can I use vertical and horizontal distances instead of a diagonal?

Yes. Enter outer vertical distance $A$ and horizontal distance $B$. The calculator computes diagonal $C$ and both cut angles automatically.

Do complementary angles always sum to 90 degrees?

Yes, for a right-triangle knee brace the two end cut angles are complementary: $\alpha + \beta = 90°$.

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Angle Cut Calculator