About the regular polygon calculator
A regular polygon has n equal sides and n equal angles. Pick the number of sides (5 for a pentagon, 6 for a hexagon, 8 for an octagon), then enter any one length or the area. The apothem r is the distance from the center to the middle of a side; the circumradius R reaches the corners.
Formulas
| Area | K = P·r/2 = n·a²/(4·tan(π/n)) |
| Circumradius | R = a/(2·sin(π/n)) |
| Apothem | r = a/(2·tan(π/n)) |
| Interior angle | θ = (n − 2)·180°/n |
Frequently asked questions
What is the area of a regular hexagon?
K = (3√3/2)·a². A hexagon with side 4 has area 24√3 ≈ 41.569.
What is the interior angle of an octagon?
(8 − 2)·180°/8 = 135°.
What is an apothem?
The perpendicular distance from the center of a regular polygon to one of its sides, the radius of the inscribed circle.