Area and perimeter of any regular polygon — instantly
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Result
6 sides · side length 5
Area
64.95190528
square units
Perimeter
30
units
| Apothem (inradius) | 4.330127units |
| Circumradius | 5units |
| Interior angle | 120° |
| Exterior angle | 60° |
| Number of diagonals | 9 |
Formulas used
Area = (n × s²) / (4 × tan(π/n))
Perimeter = n × s
Apothem = s / (2 × tan(π/n))
Circumradius = s / (2 × sin(π/n))
The Regular Polygon Area Calculator finds the area, perimeter, apothem, circumradius, and interior and exterior angles of any regular polygon — from a triangle up to a 10,000-sided shape. Simply enter the number of sides and the side length to get precise results instantly, using the standard formula Area = (n × s²) / (4 × tan(π/n)). Perfect for geometry homework, architecture, and tiling projects.
A regular polygon is a flat shape where every side has equal length and every interior angle is equal — for example, an equilateral triangle, a square, a regular hexagon, or an octagon.
The area is calculated with Area = (n × s²) / (4 × tan(π/n)), where n is the number of sides and s is the side length. This is equivalent to half the perimeter multiplied by the apothem.
The apothem is the perpendicular distance from the center of the polygon to the midpoint of any side. It equals s / (2 × tan(π/n)) and is the same as the inradius of the inscribed circle.
A circle is the limit of a regular polygon as the number of sides approaches infinity. For very large n (e.g., 10000 sides), the results closely approximate a circle with radius equal to the circumradius.