Radius Around Fenced Area

The Radius Around Fenced Area calculator computes the radius of a circle around a roughly circular fenced area (e.g., round pen) based on the number of fence sections and their length.

INSTRUCTIONS: Choose units and enter the following:

• (n) Number of Fence Sections
• (LS) Length of Fence Sections

Radius Around Fenced Area (r): The calculator returns radius and diameter in feet and inches, and the area enclosed in square yards.  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

If you want to build a roughly circular fenced area, that is good.  Mathematically, you are creating a regular polygon and enclosing the greatest amount of area with your materials by being as close to a circle as possible.  But how do you know how to space the fence segments or where to put posts?

1. Choose a center point of the fenced area.
2. Enter the number of fence segments and length of segments in this calculator to determine the radius around the fenced area. 
3. Put a stake in the ground and attach a cord or rope with the length specified in this calculator.
4. Go to the end of the rope and put in your first corner.  
5. From there use the rope to place each corner until the fenced area has been circumnavigated.

The formula for the radius of a circle around a regular polygon is:

     `r= s / (2⋅sin(πn))`

where:

• r is the radius of the circle that circumscribes the regular polygon
• s is the length of the sides of the polygon
• n is the number of sides of a polygon