MihsabaHow to use
Every side and angle of a regular polygon is equal. The side count plus one known size — side, apothem, circumradius or area — is enough to recover the rest, including angles and diagonal count.
- Enter an integer side count from 3 to 10,000.
- Choose the known measurement and enter a positive value.
- Choose the underlying length unit.
- Review area, perimeter, apothem, radius, angles and diagonal count.
How it is calculated
Example
For a regular hexagon with side 10: perimeter 60, interior angle 120°, exterior angle 60°, apothem ≈8.660, circumradius 10 and area ≈259.808.
Important notes
These formulas are for convex regular polygons, not star polygons or irregular shapes. If area is the known input, it is interpreted in the square of the selected length unit.
Frequently asked questions
What is the apothem?
The perpendicular distance from the center to a side midpoint; it is the inscribed-circle radius.
Apothem vs circumradius?
The apothem reaches a side midpoint; the circumradius reaches a vertex.
How many diagonals are there?
n(n−3)/2, counting non-adjacent vertex connections once.
Is this calculator free?
Yes. It is free to use and requires no account.