Area of a Regular Polygon Calculator
A = ¼ × n × s² × cot(π/n) for an n-gon with side length s.
Result
How to use this calculator
- Enter the number of sides (3 or more).
- Enter the side length.
- Read area, apothem, circum-radius, and perimeter.
About this calculator
A regular polygon has equal-length sides and equal interior angles. The classic formula A = ¼ n s² cot(π/n) collapses to familiar special cases — equilateral triangle (n=3): √3/4 s²; square (n=4): s²; regular hexagon (n=6): 3√3/2 s². The "apothem" is the distance from center to side midpoint.
Frequently asked
What is the apothem?+
When does the regular-polygon formula become a circle?+
What's the interior angle?+
How does this differ from area-triangle for n=3?+
Can I use this for irregular polygons?+
Related calculators
More tools you might like
Hand-picked tools that pair well with this one — same audience, same intent.
A = s² where s is the side length.
Calculate the area of a circle given its radius (or diameter). A = πr².
Three formulas: base × height ÷ 2, SAS (two sides and angle), and Heron's (three sides).
A = π × a × b, where a and b are the semi-major and semi-minor axes.
A = ½ r² θ (radians) or A = πr² × (θ/360) (degrees).
Estimate body surface area in m² using Mosteller and Du Bois formulas — for clinical reference, anesthesia dosing, and physiologic indexing.