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Polygon Calculator

Choose the polygon, select the calculation type, and enter the required parameters to calculate the missing values of the polygon using this calculator.

Choose a Regular Polygon

Side Length

Calculation with a:

m ▾

Pi π:

Related

Polygon Calculator – Area, Perimeter, and Properties

This free online polygon calculator computes all key parameters of a regular polygon. Understanding the concepts behind polygons helps you analyze their properties effectively.

What Is a Polygon?

In geometry: "A two-dimensional (2D) shape with straight sides connected at specific angles"

Polygon

Key Terms:

R = Circumradius (distance from center to a vertex)
r = Inradius (distance from center to a side)
a = Side length
n = Number of sides
x = Interior angle
y = Exterior angle
A = Area
P = Perimeter

Our polygon calculator can determine all these values from just one known parameter.

Types of Polygons

Trigon (Triangle) – 3 sides, 3 vertices
Tetragon (Quadrilateral / Square) – 4 sides
Pentagon – 5 sides
Hexagon – 6 sides
Heptagon – 7 sides
Octagon – 8 sides
Nonagon – 9 sides
Decagon – 10 sides
Undecagon – 11 sides
Dodecagon – 12 sides
Tridecagon – 13 sides
Tetradecagon – 14 sides

Polygon Formulas

For a regular polygon with n sides of length a:

Side length: a = 2r tan(π/n) = 2R sin(π/n)
Inradius: r = (a/2) cot(π/n) = R cos(π/n)
Circumradius: R = (a/2) csc(π/n) = r sec(π/n)
Area: A = (1/4) n a² cot(π/n) = n r² tan(π/n)
Perimeter: P = n a
Interior angle: x = ((n-2)/n) × 180°
Exterior angle: y = 360° / n

Example Calculation

Find the area and perimeter of a triangle (3-sided polygon) with side length 3 cm:

Area: A = (1/4) × 3 × 3² × cot(π/3) ≈ 3.89 cm²

Perimeter: P = 3 × 3 = 9 cm

How the Polygon Calculator Works

Input:

Select the polygon type
Choose a known parameter: side length, inradius, circumradius, area, or perimeter
Enter the value and unit
Click Calculate

Output:

Number of sides
Side length
Inradius
Circumradius
Area
Perimeter
Interior angle
Exterior angle

FAQs

What must a polygon have?

A polygon must have straight sides, be flat, and form a closed shape.

Is a circle a polygon?

No, a circle has no straight sides or vertices.

How many vertices are in a hendecagon?

11 vertices.

What is the sum of interior angles of a decagon?

1440°

Is an arch a polygon?

No, an arch is not a polygon.

Conclusion

Polygons are fundamental in geometry, computer graphics, and design for patterns, symmetry, and 3D modeling. Using a polygon calculator ensures accurate results for all measurements and properties.

References

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