How to use this calculator
- Enter or choose number of sides n.
- Enter or choose i know the.
- Enter or choose length.
- Enter or choose length unit.
- The area updates as you type. Use Copy result or Share to keep it.
Method
P = n·s; apothem a = s ÷ (2 tan(π/n)); R = s ÷ (2 sin(π/n)); Area = ½·P·a = n·s² ÷ (4 tan(π/n)); interior angle = (n − 2) × 180° ÷ n
- n
- number of sides
- s
- side length
- a
- apothem
- R
- circumradius
- P
- perimeter
Worked example
- Perimeter = 6 × 2 = 12 cm.
- Apothem = 2 ÷ (2 tan 30°) = √3 ≈ 1.732051 cm.
- Area = ½ × 12 × √3 = 6√3 ≈ 10.392305 cm².
A regular hexagon with 2 cm sides has an area of about 10.39 cm² and a perimeter of 12 cm.
What the result means
As n grows, the polygon approaches its circumscribed circle: a 1,000-gon’s area is within a few millionths of πR².
Assumptions and limits
- The polygon is regular and convex.
- Irregular polygons need their vertex coordinates (shoelace formula) instead.
Questions
What is the apothem?
The distance from the centre to the midpoint of any side. It is the radius of the inscribed circle.
How wide is a hexagon across the flats?
Twice the apothem; across the corners it is twice the circumradius, which for a hexagon equals two side lengths.