How It Works

This calculator helps you determine the measurements for a parallelogram brace for a gate frame:

1. Enter the width (L₁) and height (L₂) of your gate frame, along with the width of your board (typically 3.5″ for a 2×4).
2. The calculator determines the diagonal (z) using the Pythagorean theorem: z = √(L₁² + L₂²)
3. It calculates angle θ₁ between the diagonal and horizontal: tan θ₁ = L₂/L₁
4. Using the law of sines and substitution, it finds angle θ₂ (the cut angle): sin(θ₂-θ₁) = w/z
5. It calculates the x and y values: y = L₂ · x/w
6. Finally, it determines d (the inset distance): d = √(x²-w²)

The diagram shows the parallelogram brace in the context of your gate frame, with all relevant measurements labeled.

Practical Application

The parallelogram brace is commonly used in fence and gate construction because:

• Efficient Material Use: It can use a slightly shorter board than other brace designs since the hypotenuse of the frame is the diagonal of the board.
• Strong Support: The parallelogram shape provides excellent structural support against sagging and warping.
• Clean Appearance: When properly cut and installed, it creates a professional, finished look.

Installation Tips:

• Use the calculated cut angle (θ₂) to make precise cuts at both ends of your board.
• Position the board at distance d from the corner for proper alignment.
• Pre-drill holes to prevent splitting when securing the brace.
• For maximum strength, use appropriate fasteners (screws or bolts) that penetrate both the brace and the frame adequately.