N Polygon Calculator

Calculate the area, perimeter, and other properties of an n-sided polygon using our n polygon calculator. This tool helps you determine key characteristics of regular polygons with any number of sides.

What is an N Polygon?

An n polygon, or n-sided polygon, is a polygon with n sides and n vertices. Regular polygons have all sides and angles equal, while irregular polygons have sides and angles of different lengths and measures.

Common examples include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and hexagons (6 sides). This calculator works for any regular polygon with 3 or more sides.

How to Calculate Polygon Properties

Step 1: Determine the Number of Sides

First, identify how many sides your polygon has. This is the value of n in the calculator.

Step 2: Measure the Side Length

Measure the length of one side of the polygon. This is the side length (s) in the calculator.

Step 3: Calculate the Perimeter

The perimeter of a regular polygon is simply the number of sides multiplied by the length of one side.

Step 4: Calculate the Area

The area of a regular polygon can be calculated using the formula involving the apothem (the distance from the center to the midpoint of any side).

Step 5: Interpret Results

Use the calculated values to understand the size and shape of your polygon. The calculator provides both the perimeter and area for quick reference.

Formulas

The key formulas for calculating polygon properties are:

Perimeter (P) = n × s

Area (A) = (n × s²) / (4 × tan(π/n))

Apothem (a) = s / (2 × tan(π/n))

Where:

n = number of sides
s = length of one side
π = pi (approximately 3.14159)

Examples

Example 1: Square (4 sides)

For a square with side length of 5 units:

Perimeter = 4 × 5 = 20 units
Area = (4 × 5²) / (4 × tan(π/4)) ≈ 25 units²

Example 2: Pentagon (5 sides)

For a regular pentagon with side length of 3 units:

Perimeter = 5 × 3 = 15 units
Area ≈ (5 × 9) / (4 × tan(π/5)) ≈ 13.4 units²

FAQ

What is the difference between a regular and irregular polygon?

A regular polygon has all sides and angles equal, while an irregular polygon has sides and angles of different lengths and measures.

Can this calculator work for polygons with more than 10 sides?

Yes, the calculator works for any regular polygon with 3 or more sides.

What units should I use for side length?

You can use any unit of length (meters, inches, centimeters, etc.) as long as you're consistent throughout your calculations.