Regular polygon calculator

Enter the number of sides and length of the regular polygon, and click "Calculate".
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The figure above is a regular octagon

The blue circle outside is called the circumcircle and the red circle is called the incircle.

Angle EAB is an inner angle

of the regular octagon

Angle EAF is an external angle of the regular octagon and it is equal to the central angle ACB.

AC is the radius of the circumcircle.

CD is the radius of the incircle.

A Regular Polygon Calculator is a tool used to calculate various properties of regular polygons. A regular polygon is a polygon with all sides and all angles equal, such as a square, equilateral triangle, or regular pentagon.

What Is a Regular Polygon Calculator?

A Regular Polygon Calculator helps you find different measurements and properties of a regular polygon based on specific parameters, such as:

  • Number of sides (n)
  • Side length (s)
  • Apothem (the distance from the center of the polygon to the midpoint of any side)
  • Area
  • Perimeter
  • Interior angle

Why Use a Regular Polygon Calculator?

Regular polygons are commonly used in geometry, architecture, art, and design, so being able to calculate their properties easily and accurately is useful. The regular polygon calculator makes these calculations faster and more accurate, which is especially helpful in:

  • Mathematics: Solving geometry problems related to polygons.
  • Architecture and Engineering: Designing structures with regular polygons, such as tiles, floor plans, or roofs.
  • Art and Design: Creating patterns, especially those involving symmetry.

How Does a Regular Polygon Calculator Work?

To use a regular polygon calculator, you'll typically need to input certain known values. These might include:

  1. Number of sides (n): The number of sides of the polygon (e.g., 3 for a triangle, 4 for a square, 6 for a hexagon).
  2. Side length (s): The length of one of the sides of the polygon.
  3. Apothem (a): The perpendicular distance from the center of the polygon to the midpoint of one of its sides.

The calculator then uses specific formulas to compute various properties, such as:

  • Perimeter: P=n×s

    • The perimeter is simply the sum of the lengths of all sides.

  • Area: A=1/2×n×s×a

    • The area can be calculated using the number of sides, side length, and apothem.

  • Interior angle:

    • The interior angle is the angle formed between two adjacent sides at a vertex of the polygon.

  • Circumradius (R):

    • The radius of the circle that circumscribes the regular polygon.

  • Inradius (r):

    • The radius of the circle inscribed inside the regular polygon.

When Should You Use a Regular Polygon Calculator?

A regular polygon calculator is useful when you need to calculate the properties of a regular polygon in a variety of situations, such as:

  • Mathematical problems: When solving geometry or trigonometry problems involving regular polygons.
  • Design and Architecture: When creating patterns or structures involving regular polygons, such as tiling, circular windows, or design patterns.
  • Art and Symmetry: When working with symmetry and geometric designs in art, like mandalas, tiling patterns, or geometric decorations.