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?
- Choose a center point of the fenced area.
- Enter the number of fence segments and length of segments in this calculator to determine the radius around the fenced area.
- Put a stake in the ground and attach a cord or rope with the length specified in this calculator.
- Go to the end of the rope and put in your first corner.
- 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