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How do I calculate the diameter or radius of an arc?

 

If you know two of the following about an arc, you can calculate the diameter or radius for that arc.

  • Segment Height (rise)
  • Chord Length (run) of an arc.
  • Arc Angle

Here are some examples:

Example 1:
Find the radius of an arc given a Segment Height (Rise) of 2m and a Chord Length (Run) of 6m

You Input
[clr]
[clr]
6
[m]
[Run]
2 [m] [Rise]
[Conv]
[Radius]
BuildCalc Displays
0
6m
Run

6m

Rise

2m

Radius

3.25m

Example 2:  Find the diameter of an arc given a Segment Height (Rise) of 6ft 2in and a Chord Length (Run) of 20ft 6in

Your Input
[clr]
[clr]
6
[Feet] 2 [in]
[Rise]
20 [Feet] 6 [Inch] [Run]
[Circle]
BuildCalc Displays
0
6ft 2in
Run

6ft 2in

Rise

20ft 6in

Diameter

23ft 2- 7/16in

Example 3:  Find the radius and diameter of an arc given a Chord Length (Run) of 36 inch and a 30° arc angle.

You Input
[clr]
[clr]
36
[Inch] [Run]
30
[Arc]
[Conv]
[Radius]
[Circle]
BuildCalc Displays
0
Run

36in

Arc Angle

30.00°

Radius

69- 9/16in

Diameter

139- 1/16in

Note that the [Arc] function can be used to calculate the length of each stud required to frame an arch.

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