How is the area of a regular polygon calculated?

Area = (n × s²) ÷ (4 × tan(π ÷ n)), where n is the number of sides and s is the side length. Every side is equal in a regular polygon.

The apothem is the perpendicular distance from the centre of the polygon to the midpoint of a side. It equals the radius of the inscribed circle.

How do I find the interior angle of a regular polygon?

Each interior angle is (n − 2) × 180 ÷ n degrees. A triangle gives 60°, a square 90°, a pentagon 108° and a hexagon 120°.

What is the circumradius?

The circumradius is the distance from the centre to a vertex — the radius of the circle that passes through every corner. It equals s ÷ (2·sin(π ÷ n)).

What is the difference between the apothem and the circumradius?

The apothem reaches the midpoint of a side (inscribed circle), while the circumradius reaches a vertex (circumscribed circle). The circumradius is always the larger of the two.

How many sides can I enter?

Any number of sides from 3 upward. As the side count grows with a fixed side length, the polygon approaches a circle and its area increases.

Is my data sent anywhere?

No — every calculation runs locally in your browser and nothing is uploaded.

Polygon Area Calculator

Regular polygon calculator

Enter the number of sides and the side length of any regular polygon and this tool returns its area, perimeter, interior angle, apothem (inradius) and circumradius. A regular polygon has equal sides and equal angles, so a few formulas describe every triangle, square, pentagon, hexagon and beyond — useful for geometry, tiling and design.

How it works

With n sides of length s, the tool uses the standard regular-polygon formulas (angles in radians where π/n appears):

area           = (n × s²) ÷ (4 × tan(π ÷ n))
perimeter      = n × s
interior angle = (n − 2) × 180 ÷ n   degrees
apothem        = s ÷ (2 × tan(π ÷ n))
circumradius   = s ÷ (2 × sin(π ÷ n))

Example

A regular hexagon (n = 6) with side = 10:

Perimeter: 6 × 10 = 60
Interior angle: (6 − 2) × 180 ÷ 6 = 120°
Apothem: 10 ÷ (2·tan30°) ≈ 8.66
Circumradius: 10 ÷ (2·sin30°) = 10
Area: (6 × 100) ÷ (4·tan30°) ≈ 259.81

Sides	Shape	Interior angle	Area (side 10)
3	Triangle	60°	43.30
4	Square	90°	100
6	Hexagon	120°	259.81

Everything is computed in your browser — no data leaves your device.