a regular hexagon
- Number of sides
- 6
- Side length
- 5
Area64.95
Interior angle 120 by the (n-2)180/n rule
Open this exampleMath & Statisticsgeometry
Polygon Calculator
Regular polygon area, angles and radii. As the side count rises the shape approaches a circle, which the apothem and circumradius converging makes visible.
Also called: regular polygon area, hexagon calculator.
Area
64.95
A regular 6-sided polygon of side 5 has area 64.95 and perimeter 30. Each interior angle is 120 degrees.
Perimeter
30
Interior angle (degrees)
120
Exterior angle (degrees)
60
Apothem
4.33
Circumradius
5
Method and background
How this is calculated
A regular polygon splits into n identical triangles from the centre, which gives the area formula. The interior angle depends only on the side count, not the size. The apothem is the distance from centre to the middle of a side and the circumradius to a corner; they converge as the side count grows, which is exactly the sense in which a polygon becomes a circle.
area of a regular polygon from side count and side length; interior angle from the side count alone- n
- Number of sides
- s
- Side length
Worked examples
Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.
a triangle is the smallest polygon
- Number of sides
- 3
- Side length
- 5
Area10.83
boundary
Open this exampleMethod and limits
What it assumes
- A regular polygon with equal sides and angles.
What it deliberately does not model
- Irregular polygons need the shoelace formula on their coordinates instead.
Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator
Frequently asked questions
- Why do exterior angles always sum to 360?
- Because walking the perimeter turns you through one full circle regardless of the side count. Each exterior angle is therefore 360 divided by the number of sides.