Regular Polygon Calculator
Compute every key measurement of a regular polygon — area, perimeter, angles, apothem and circumradius — from just the number of sides and one side length.
units
Area enclosed by the regular polygon
- 1
Interior angle = (n − 2) × 180 ÷ n
(6 − 2) × 180 ÷ 6 = 120° - 2
Perimeter = n × s
6 × 10 = 60 - 3
Apothem = s ÷ (2 × tan(π ÷ n))
10 ÷ (2 × tan(π ÷ 6)) = 8.6603The perpendicular distance from the center to any side. - 4
Area = perimeter × apothem ÷ 2
60 × 8.6603 ÷ 2 = 259.8076
How does this calculator work?
Enter the number of sides (n ≥ 3) and one side length s. The calculator returns area = ¼·n·s²·cot(π/n), perimeter n·s, interior angle (n−2)·180/n, exterior angle 360/n, apothem s/(2·tan(π/n)) and circumradius s/(2·sin(π/n)), plus a scaled drawing of the polygon.
Formula
How this is calculated
A regular polygon has n equal sides of length s and n equal angles. From these two inputs every other property follows. The interior angle is (n−2)·180/n degrees because the sum of interior angles of any n-gon is (n−2)·180°, shared equally; the exterior angle is its supplement, 360/n.
The apothem — the perpendicular distance from the center to a side — is a = s/(2·tan(π/n)). The perimeter is simply P = n·s, and the area equals half the perimeter times the apothem, Area = P·a/2, which simplifies to ¼·n·s²·cot(π/n). The circumradius R = s/(2·sin(π/n)) is the distance from the center to each vertex.
Inputs must satisfy n ≥ 3 (a polygon needs at least three sides) and s > 0. Angles are reported in degrees; lengths and the apothem share the same unit as s, and area is in those units squared. As n grows the polygon approaches a circle, so the area approaches πR². The plot places vertices at R·(cos θ, sin θ) for θ = 2πk/n to show the actual shape.
Frequently asked questions
The apothem is the perpendicular distance from the polygon's center to the midpoint of any side. It equals s/(2·tan(π/n)) and is used to compute area as half the perimeter times the apothem.
A closed polygon needs a minimum of three sides; with two or fewer sides no enclosed area exists, so the formulas are undefined for n < 3.
The apothem reaches the middle of a side (inradius), while the circumradius reaches a vertex. The circumradius is always larger; both converge to the same circle radius as the number of sides increases.
Also known as
TG we-Calculate Editorial Team. (2026). Regular Polygon Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/regular-polygon-calculator
TG we-Calculate Editorial Team. "Regular Polygon Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/regular-polygon-calculator.
TG we-Calculate Editorial Team, "Regular Polygon Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/regular-polygon-calculator
@misc{wecalculate_regular_polygon_calculator, title = {Regular Polygon Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/regular-polygon-calculator}}, year = {2026}, note = {TG we-Calculate} }
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