Polygon Calculator
Calculate the properties of regular polygons including side length, inradius (apothem), circumradius, area, perimeter, and interior/exterior angles. Enter any one property to calculate all others.
Polygon Properties
| Number of Sides | 5 |
|---|---|
| Side Length | 1.00 |
| Inradius (Apothem) | 0.69 |
| Circumradius | 0.85 |
| Area | 1.72 |
| Perimeter | 5.00 |
| Interior Angle | 108.00° |
| Exterior Angle | 72.00° |
About Polygon Calculator
A regular polygon is a geometric shape with all sides and all angles equal. This calculator helps you find all the properties of a regular polygon when you know just one property (like side length, area, or radius).
Polygon Formulas
The following formulas are used to calculate the properties of regular polygons:
- Interior Angle: (n-2) × 180° / n
- Exterior Angle: 360° / n
- Inradius (Apothem): a = s / (2 × tan(π/n))
- Circumradius: R = s / (2 × sin(π/n))
- Area: A = (1/2) × n × s × a = (1/2) × perimeter × a
- Perimeter: P = n × s
Where n is the number of sides and s is the side length.
Common Regular Polygons
Some of the most common regular polygons include:
- Equilateral Triangle (3 sides): All angles are 60°
- Square (4 sides): All angles are 90°
- Regular Pentagon (5 sides): Each interior angle is 108°
- Regular Hexagon (6 sides): Each interior angle is 120°
- Regular Heptagon (7 sides): Each interior angle is ~128.57°
- Regular Octagon (8 sides): Each interior angle is 135°
Applications of Regular Polygons
Regular polygons have many practical applications:
- Architecture: Used in floor plans, tiling, and structural designs
- Engineering: Used in gear design and mechanical components
- Nature: Seen in honeycombs (hexagons) and crystal structures
- Art and Design: Used in patterns, logos, and decorative elements
- Computer Graphics: Used as basic shapes in 3D modeling