Regular Polygon Calculator
Calculate area, perimeter, apothem, circumradius, and angles of any regular polygon.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Request a ToolHow to Use the Regular Polygon Calculator
Enter the number of sides and the side length. The calculator computes the area, perimeter, apothem, circumradius, interior angle, and exterior angle.
- Enter the number of sides. Must be 3 or more (3 = triangle, 4 = square, 5 = pentagon, 6 = hexagon, etc.).
- Enter the side length. The length of each equal side.
- Read the results. Area is the primary result. All other properties appear in the breakdown.
About Regular Polygons
A regular polygon has all sides equal and all interior angles equal. The area formula is (n * s^2) / (4 * tan(pi/n)), where n is the number of sides and s is the side length. The interior angle of a regular n-gon is ((n-2) * 180) / n degrees. The exterior angle is always 360/n degrees. As the number of sides increases, a regular polygon approaches a circle. Regular polygons are important in geometry, architecture, tiling, and engineering.
Frequently Asked Questions
What is the interior angle of a regular polygon?
The interior angle is ((n-2) * 180) / n degrees, where n is the number of sides. A regular hexagon (n=6) has interior angles of 120 degrees.
What is the apothem of a regular polygon?
The apothem is the perpendicular distance from the center to the midpoint of a side. It equals s / (2 * tan(pi/n)), where s is the side length and n is the number of sides.
What is the circumradius?
The circumradius is the distance from the center to any vertex. It equals s / (2 * sin(pi/n)). A circle with this radius passes through all vertices of the polygon.