About this tool
Enter the number of sides and the side length of a regular (equal-sided, equal-angled) polygon to get its full set of geometric properties at once. Everything is worked out live in your browser and nothing is uploaded.
For a polygon with n sides of length a, the area is (n · a²) / (4 · tan(π/n)), the perimeter is n · a, the apothem (center-to-edge distance) is a / (2 · tan(π/n)) and the circumradius (center-to-vertex distance) is a / (2 · sin(π/n)). Each interior angle equals (n − 2) · 180 / n degrees, each exterior angle is 360 / n degrees, and the number of diagonals is n(n − 3) / 2.
Use it to plan tilework, nuts and bolts, gears, game boards or any shape built from a repeated regular polygon. Common shapes such as the triangle, square, pentagon and hexagon are named automatically.