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Polygon Side around a Circle

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Last modified by
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Aug 8, 2023, 1:35:11 PM
Created by
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Feb 25, 2015, 7:47:21 PM
s=2rtan(πn)
(n) Number of Sides
(r) Radius
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1d2adf4e-bd27-11e4-a9fb-bc764e2038f2

The Length of a Side of a Regular Polygon calculator computes the length of the individual sides (segments) of a regular polygon given the number of sides and the radius, r, of an inscribed circle./attachments/1d2adf4e-bd27-11e4-a9fb-bc764e2038f2/PolyCi.png

INSTRUCTIONS: Choose units and enter the following:

  • (r) Inner Radius
  • (n) Number of Sides of Polygon

Polygon Side Length (s):  The calculator returns the length of the side in meters.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

A regular n-sided polygon is a polygon with n equal length sides and has n equal angles at the n vertices of the polygon.  Because of the symmetries of this construction, the sides of the polygon touch the inscribed circle as tangents at the midpoint of the polygon side.  As shown in the picture, Figure 1, lines from the vertices to the circle's center form n isosceles triangles of equal area.

The formula for the length of a side of a polygon based on the inner radius and number of sides is:

        s = 2•r•tan(π/n)

where:


Regular Polygon Information

A regular polygon is a geometric shape with three or more straight sides where every side is the same length and every angle between connecting sides are the same angle. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length .  Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side.  As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form n isosceles triangles of equal area.

The names of polygons vary based on the number of sides as follows:

  • triangle - 3 sides
  • square - 4 sides 
  • pentagon - 5 sides
  • hexagon - 6 sides
  • heptagon - 7 sides
  • octagon - 8 sides
  • nonagon - 9 sides
  • decagon - 10 sides
  • hendecagon - 11 sides
  • dodecagon - 12 sides

Common Regular Polygon Functions

Polygon Area Calculators:

Polygon Side Calculators

Polygon Perimeter Calculators

Polygon Radius

3D Polygon Shapes

Other Polygon Calculators


This equation, Polygon Side around a Circle, is used in 3 pages
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