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Sides of a Regular Polygon
The sides of a regular polygon are the line segments that make it up.
Try this Adjust the regular polygon below by dragging any orange dot, or alter the number of sides. The length of the sides will change.

The formulas below give the length of the side of regular polygon given the number of sides and either the radius or apothem.

Side length given the apothem (inradius)

If you know the apothem (distance from the center of the polygon to the midpoint of any side - see figure above)

where:
a  is the length of the apothem (inradius)
n  is the number of sides
tan  is the tangent function calculated in degrees
(see Trigonometry Overview)



Side length given the radius (circumradius):

If you know the radius (distance from the center to a vertex):
where:
r  is the radius (circumradius)
n  is the number of sides
sin  is the sine function calculated in degrees
(see Trigonometry Overview)


Irregular polygons

The sides of an irregular polygon are essentially random lengths. There is no formula to calculate their lengths. In the figure above, uncheck 'regular' to see this.

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons

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