Regular Polygon Area Calculator

Work out regular polygon area instantly with clear inputs, formula shown and shareable results.

About Regular Polygon Area Calculator

A regular n-gon divides into n identical isosceles triangles from its centre. Each has base s and height equal to the apothem s/(2·tan(π/n)), so the total area is n·s² / (4·tan(π/n)).

Formulas

Regular polygon area

A = n·s² / (4·tan(π/n))

Apothem

a = s / (2·tan(π/n))

Worked example

With the default values below, Regular Polygon Area Calculator returns Area of 64.9519. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of sidesaccepts 3–1,000: 6
Side lengthminimum 0: 5

Results

Area: 64.9519
Perimeter: 30.0000
Apothem (inradius): 4.3301
Circumradius: 5.0000

Step by step

1Values used
2Regular polygon area
3Apothem
4Area= 64.9519
5Perimeter= 30.0000
6Apothem (inradius)= 4.3301
7Circumradius= 5.0000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What happens as n grows?

The polygon approaches a circle of radius equal to the circumradius, and the area tends to πR².

Can I use A = ½ × perimeter × apothem?

Yes, that is the same formula rearranged and is often easier to remember.