Regular Polygon Calculator (Angles, Area, Perimeter)
By Santaji GadepatilinUpdated October 27, 2026
A regular polygon has equal sides and equal angles. Its area, perimeter and angles all follow from the number of sides and one length.
How to use the regular polygon calculator
Enter the number of sides and the side length. The calculator shows the angles, number of diagonals, perimeter and area of the regular polygon. The angle results apply to any polygon with that number of sides; the area and perimeter assume all sides and angles are equal.
Regular polygon formulas
| Quantity | Formula |
|---|---|
| Sum of interior angles | (n − 2) × 180° |
| Each interior angle | (n − 2) × 180° ÷ n |
| Each exterior angle | 360° ÷ n |
| Diagonals | n(n − 3) ÷ 2 |
| Area | n × s² ÷ (4 tan(π ÷ n)) |
Polygon table
| Polygon | Sides | Interior angle | Diagonals | Area (side 1) |
|---|---|---|---|---|
| Triangle | 3 | 60.00° | 0 | 0.4330 |
| Square | 4 | 90.00° | 2 | 1.0000 |
| Pentagon | 5 | 108.00° | 5 | 1.7205 |
| Hexagon | 6 | 120.00° | 9 | 2.5981 |
| Heptagon | 7 | 128.57° | 14 | 3.6339 |
| Octagon | 8 | 135.00° | 20 | 4.8284 |
| Nonagon | 9 | 140.00° | 27 | 6.1818 |
| Decagon | 10 | 144.00° | 35 | 7.6942 |
| Dodecagon | 12 | 150.00° | 54 | 11.1962 |
Multiply the last column by the side length squared to get the area.
Hexagons in nature and design
Regular hexagons tile a flat surface with no gaps and use the least perimeter for a given area among shapes that tile, which is why honeycombs and many floor tiles are hexagonal.
Radius of a regular polygon
- Circumradius (centre to corner): R = s ÷ (2 sin(π ÷ n))
- Inradius (centre to middle of a side): r = s ÷ (2 tan(π ÷ n))
As n grows large, the polygon approaches a circle.
Frequently asked questions
What is the sum of interior angles of a polygon?
(n − 2) × 180°. A hexagon (6 sides) has 720°, so each angle of a regular hexagon is 120°.
How many diagonals does a polygon have?
n(n − 3) ÷ 2. An octagon has 20 diagonals.
What is the area of a regular hexagon?
(3√3 ÷ 2) × s², about 2.598 × s². With 10 cm sides, about 259.8 cm².
Do exterior angles always add to 360°?
Yes, for any convex polygon the exterior angles sum to 360°.