Side Length of N Gon Calculator
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Reviewed by Calculator Editorial Team
A regular n-sided polygon (n-gon) is a polygon with n equal sides and n equal angles. This calculator determines the side length of a regular n-gon when given either the perimeter or the circumradius.
What is an N-gon?
A regular n-gon is a polygon with n sides where all sides are equal in length and all interior angles are equal. Common examples include equilateral triangles (3-gons), squares (4-gons), regular pentagons (5-gons), and regular hexagons (6-gons).
Regular n-gons are used in architecture, engineering, and design due to their symmetry and predictable properties. The side length is a fundamental property that determines the polygon's size and shape.
Formula for Side Length
The side length (s) of a regular n-gon can be calculated using two main formulas:
When perimeter is known:
s = Perimeter / n
Where:
- s = side length
- Perimeter = total distance around the polygon
- n = number of sides
When circumradius is known:
s = 2 × R × sin(π/n)
Where:
- s = side length
- R = circumradius (distance from center to a vertex)
- n = number of sides
The calculator uses these formulas to provide accurate results based on your input.
How to Use the Calculator
- Enter the number of sides (n) of your polygon.
- Choose whether you know the perimeter or the circumradius.
- Enter the known value in the appropriate field.
- Click "Calculate" to determine the side length.
- Review the result and use the chart to visualize the relationship between sides and perimeter.
Worked Examples
Example 1: Square (4-gon)
Given a square with perimeter 20 units:
Side length = 20 / 4 = 5 units
Example 2: Regular Hexagon (6-gon)
Given a regular hexagon with circumradius 10 units:
Side length = 2 × 10 × sin(π/6) ≈ 2 × 10 × 0.5 = 10 units
| Polygon | Perimeter | Side Length |
|---|---|---|
| Equilateral Triangle (3-gon) | 18 units | 6 units |
| Square (4-gon) | 20 units | 5 units |
| Regular Pentagon (5-gon) | 25 units | 5 units |
FAQ
What is the difference between a regular and irregular n-gon?
A regular n-gon has all sides and angles equal, while an irregular n-gon has sides and angles of different measures.
Can I use this calculator for non-integer values of n?
Yes, the calculator accepts any positive real number for n, though polygons with non-integer sides are typically theoretical.
What is the smallest possible n-gon?
The smallest n-gon is a digon (n=2), though it's not commonly used in practical applications.