Regular Polygon Calculator: Angles, Area, Perimeter and Apothem
Enter how many sides the polygon has and the length of one side. Everything else is worked out, from the angles to the area.
- Nothing you type is stored
- Free
- No signup
Area
64.9519cm²
Hexagon- Each interior angle
- 120 °
- Each exterior angle
- 60 °
- Perimeter
- 30 cm
- Apothem (a)
- 4.3301 cm
- Circumradius (R)
- 5 cm
- Diagonals
- 9
Show working
- Interior angle = (n − 2) × 180° / n = 4 × 180 / 6 = 120°
- Exterior angle = 360° / n = 60°
- P = n × s = 6 × 5 = 30 cm
- a = s / (2 tan(180°/n)) = 4.3301 cm
- A = ½ × P × a = ½ × 30 × 4.3301 = 64.9519 cm²
How to use
- Enter the number of sides n (3 or more).
- Enter the side length and pick a unit.
- Read the area, angles, apothem and other values.
Good to know
In a regular polygon all sides and angles are equal. Each exterior angle is 360°/n and each interior angle is (n − 2) × 180°/n. The sum of exterior angles is always 360°, as NCERT Class 8 "Understanding Quadrilaterals" shows.
The apothem is the distance from the centre to the middle of a side: a = s / (2 tan(180°/n)). Area = ½ × perimeter × apothem. The circumradius (centre to a corner) is s / (2 sin(180°/n)).
Number of diagonals = n(n − 3)/2. A common exam question works backwards: if each interior angle is 140°, the exterior angle is 40° and n = 360 ÷ 40 = 9.
Questions
What is the interior angle of a regular hexagon?
(6 − 2) × 180° ÷ 6 = 120°.
How do I find the number of sides from an angle?
n = 360° ÷ exterior angle, and exterior angle = 180° − interior angle.
What is an apothem?
The perpendicular distance from the centre to a side. It is the radius of the circle drawn inside the polygon.
How many diagonals does an octagon have?
8 × 5 ÷ 2 = 20.
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.