How to Find the Radius of a Curve With a Framing Square

Remodeling and fabrication jobs that involve curves are often difficult for carpenters and woodworkers accustomed to straight lines and crisp, clean right angles. To copy an existing curve accurately, you need to determine its radius. Doing so seems especially troublesome when only a section of the arc is present. With the help of a carpenter's framing square and a mathematical formula, you can make this calculation quickly and accurately.

Framing square
Pencil
Calculator (optional)

Instructions

- 1
  Place one arm of the square inside the arc so that one edge completely crosses the circle and the other side just touches the arc. Make a pencil tick mark at the point where the arm touches the arc and draw a line across the circle on the other side.
- 2
  Measure and record L, the length of the line that crosses the circle. Use the two arms of the square to draw a second line through the tick mark at right angles to the first line. Measure and record H, the distance between the first line and the tick mark. For example, L = 24 and H = 2.
- 3
  Divide L by two and square the result; then divide the answer by H. For example, 24 / 2 = 12; 12 squared = 144; 144 divided by 2 = 72.
- 4
  Add H to the previous result and divide the sum by 2. The result is the radius of the circle. For example, 72 + 2 = 74; divided by 2 = 37. The radius is 37.

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