Regular Polygon Area Calculator
Find the area, perimeter and angles of any regular polygon.
Results update as you type.
How it works
A regular polygon has all sides and all angles equal, and this calculator finds the area, perimeter, and interior angle of any regular polygon from the number of sides and the side length. You enter how many sides the shape has, three or more, and the length of each side, and it returns all three quantities. The area formula divides the polygon into identical triangles radiating from the centre and sums them, giving n times the side squared over four times the tangent of pi divided by n. As the number of sides grows, a regular polygon looks more and more like a circle, and its area approaches that of the circle with the same perimeter. The perimeter is simply the number of sides times the side length, and each interior angle equals two less than the number of sides, times 180, divided by the number of sides, so a triangle has 60 degrees, a square 90, a hexagon 120, and so on. This single tool replaces separate formulas for triangles, squares, pentagons, hexagons, octagons, and beyond. Enter the number of sides and the side length to compute the area, perimeter, and interior angle.
Area = (n·s²) / (4·tan(π/n))
The area of a regular polygon with n sides of length s is n times the side squared, divided by four times the tangent of pi over n. This comes from splitting the polygon into n identical isosceles triangles. The perimeter is n times the side, and each interior angle is (n minus two) times 180 divided by n degrees.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter number of sides (n) and side length.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Area updates instantly as you type — no button to press.
Frequently asked questions
What is a regular polygon?
A regular polygon is a closed shape with straight sides in which every side has the same length and every interior angle is equal. Examples include the equilateral triangle, the square, the regular pentagon, and the regular hexagon. This calculator works for any regular polygon with three or more sides.
How do you find the area of a regular polygon?
Use the formula: the number of sides times the side length squared, divided by four times the tangent of pi divided by the number of sides. This works by dividing the polygon into equal triangles from its centre. Enter the number of sides and side length, and the calculator evaluates this formula automatically.
What is the interior angle formula?
Each interior angle of a regular polygon equals two less than the number of sides, multiplied by 180, then divided by the number of sides. A triangle gives 60 degrees, a square 90, a pentagon 108, and a hexagon 120. The interior angles increase toward 180 degrees as the number of sides grows.
Why does a polygon approach a circle?
As a regular polygon gains more sides of the same total perimeter, its shape hugs a circle ever more closely, and its area approaches the circle's area. In the limit of infinitely many sides, the polygon becomes a circle. This is the geometric idea behind the classical approximations of pi using inscribed polygons.
What is the minimum number of sides?
A polygon must have at least three sides to enclose an area, so the smallest regular polygon is the equilateral triangle. Values below three are not valid polygons, and this calculator requires three or more sides. There is no upper limit; as the count rises, the polygon increasingly resembles a circle.