Regular Polygon Area
Compute the area of any regular polygon from its side length and number of sides using A = (n x s^2) / (4 x tan(pi/n)). Free online geometry tool for n-gons.
About This Calculator
Use this regular polygon area calculator to quickly find the area of any regular polygon -- from equilateral triangles and squares to regular pentagons, hexagons, octagons, and beyond. A regular polygon is a shape where all sides have equal length and all interior angles are equal.
The area is computed using the formula A = (n x s^2) / (4 x tan(pi/n)), where n is the number of sides and s is the side length. This formula derives from dividing the polygon into n congruent isosceles triangles from the center, computing one triangle's area, and multiplying by n. The tangent function adjusts for how the polygon's shape changes with the number of sides.
Regional Notes: This calculator works with any unit system (metric or imperial). Enter lengths in meters, centimeters, inches, feet, or any unit, and the area result is reported in the corresponding square units. Geometry formulas are universal and do not vary by region.
Frequently Asked Questions
What is the formula for regular polygon area?
The area of a regular polygon is A = (n x s^2) / (4 x tan(pi/n)), where n is the number of sides and s is the side length. For a regular hexagon with side 5, area = (6 x 25) / (4 x tan(30 deg)) = 150 / (4 x 0.577) = 64.95 square units.
Can I use this calculator for any regular polygon?
Yes, this calculator works for any regular polygon with 3 or more sides, including equilateral triangles, squares, regular pentagons, hexagons, heptagons, octagons, and any n-sided regular polygon. Simply enter the number of sides and the side length.
What units should I use for side length?
You can use any unit of length such as meters, centimeters, inches, feet, or yards. The area result will be in the corresponding square unit. For example, side length in meters gives area in square meters; side length in inches gives area in square inches.
How does the number of sides affect the area?
For a fixed side length, increasing the number of sides increases the area. A regular decagon (10 sides) with side length 5 has a larger area than a regular pentagon (5 sides) with the same side length. As n approaches infinity, the polygon approaches a circle.
What is the difference between a regular and irregular polygon?
A regular polygon has all sides equal and all interior angles equal, like a square or equilateral triangle. An irregular polygon has sides of different lengths or angles of different measures. This calculator is designed exclusively for regular polygons.
Can I calculate the area if I know the apothem or circumradius instead of side length?
This calculator uses side length and number of sides. If you know the apothem (inradius), use area = n x apothem^2 x tan(pi/n). If you know the circumradius, use area = (n/2) x R^2 x sin(2pi/n). Alternative formulas exist for different known parameters.
Is the Regular Polygon Area Calculator free to use?
Yes, all calculators on Calculy are completely free to use. No registration, login, or payment is required. You can bookmark any calculation with shareable URLs that preserve your inputs.