Regular Polygon Area Calculator
Find the exact area of any regular polygon from its number of sides and side length, using the apothem-and-perimeter formula.
How it works
Area = ½ · perimeter · apothem · Apothem = s ÷ (2·tan(π/n)) · Perimeter = n·s
A regular polygon can be split into n identical isosceles triangles that meet at the centre. Each triangle has base s and height equal to the apothem — the perpendicular distance from the centre to a side — so the total area is one half of the perimeter times the apothem. The apothem itself comes from the fact that the angle at the centre of each triangle is 2π/n.
Worked example
For a regular hexagon (n = 6) with side 10: apothem = 10 ÷ (2·tan(30°)) = 10 ÷ 1.1547 = 8.660, perimeter = 60, so area = ½ · 60 · 8.660 = 259.8 square units.
Sources: Regular polygon — Wikipedia
Frequently asked questions
What counts as a regular polygon?
A regular polygon has all sides equal in length and all interior angles equal. Squares and equilateral triangles are regular; a generic rectangle is not, because its sides are not all equal.
Why is the apothem needed?
The apothem is the height of each of the n triangles the polygon divides into. Multiplying half the base (side) by the apothem gives one triangle’s area, and n of them make the whole polygon — which simplifies to ½ · perimeter · apothem.
Does this work for a circle?
As the number of sides grows very large, a regular polygon approaches a circle and this formula approaches πr². For an actual circle, use a dedicated circle calculator instead.
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This calculator is for educational purposes. Double-check important results before acting on them.