Polygon Properties Calculator

A regular polygon has all sides equal in length and all interior angles equal. Regular polygons with 3, 4, 5, and 6 sides are called triangles, squares, pentagons, and hexagons.

As the number of sides increases, the polygon increasingly resembles a circle. This observation is the foundation of Archimedes' method for approximating pi.

The sum of interior angles of any n-sided polygon is $(n-2) \times 180^\circ$. For a regular polygon, each interior angle is

Each exterior angle is $\frac{360^\circ}{n}$. Interior and exterior angles at any vertex always sum to 180°.

The area of a regular polygon can be computed from the number of sides $n$ and side length $s$.

Alternatively, using the apothem $a$ and perimeter $P$: $A = \frac{1}{2}\,a\,P$.

The apothem is the distance from the center to the midpoint of a side. The circumradius is the distance from the center to a vertex.

The inscribed circle (tangent to all sides) has radius equal to the apothem. The circumscribed circle (passing through all vertices) has radius equal to the circumradius.