The Length of Polygon Side calculator computes the length of the individual sides (segments) of a regular polygon given the number of sides of the regular polygon and the radius, r, of a circumscribed (outer) circle.
INSTRUCTIONS: Choose units and enter the following:
- (r) Outer Radius
- (n) Number of sides of the polygon
Polygon Side Length (s): The calculator returns the length of the sides 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 is a polygon which has n equal angles at the n vertices of the polygon. Because of the symmetry of this construction, all the vertices of the regular polygon lie on the circle and the sides of the regular polygons form n chords of the circle.
The formula for the length of a side of a polygon based on the outer radius and number of sides is:
where:
- s is the length of the sides of a polygon inside of the circle
- r is the radius of the outer circle
- n is the number of sides (integer)
Polygon Calculators:
- Area of a Polygon based on the length and number of sides.
- Area of a Polygon based on the number of sides and the outer radius.
- Area of a Polygon based on the number of sides and the inner radius.
- Perimeter of a Polygon based on the number and length of sides.
- Perimeter of a Polygon based on the number of sides and the outer radius.
- Perimeter of a Polygon based on the number of sides and the inner radius.
- Length of a Polygon Side based on Circumscribed Circle Radius
- Length of a Polygon Side based on Inscribed Circle Radius