💠 Polygon Calculator
Calculate precise properties for any regular polygon with 3 or more sides.
Properties
- Area = (n × s²) / (4 × tan(π/n))
- Perimeter = n × s
- Sum of Interior Angles = (n-2) × 180°
- Interior Angle = Sum / n
- Exterior Angle = 360° / n
- Central Angle = 360° / n
The Comprehensive Guide to Regular Polygon Calculator
What is a Regular Polygon Calculator?
A Polygon Calculator is a universal geometric solver capable of determining the physical dimensions and angular properties of any regular polygon with three or more sides (n ≥ 3).
Instead of requiring a different calculator for a Pentagon (5), Nonagon (9), or Dodecagon (12), you simply input the number of sides (n) alongside one known metric (like side length or area), and the tool reverse-calculates the exact area, perimeter, internal angles, and radii utilizing trigonometric functions.
The Mathematical Formula
This tool utilize standardized mathematical formulas and logic to calculate precise Polygon results.
Calculation Example
Let's calculate the Interior Angle of a regular Dodecagon (a 12-sided polygon):
- Formula: Total Sum / n = [(n - 2) × 180°] / n
- Angle = [(12 - 2) × 180°] / 12
- Angle = [10 × 180°] / 12
- Angle = 1800° / 12
- Single Interior Angle = 150°
Strategic Use Cases
- 3D Modeling & CAD: Instantly calculating circumradius dimensions to ensure a many-sided custom gear or circular approximation fits exactly within a mechanical housing.
- Mathematics Education: Visually proving to students how, as the number of sides (n) approaches infinity, the Area and Perimeter formulas of a polygon naturally converge into the Area (πr²) and Circumference (2πr) of a circle.
- Architecture: Designing gazebo floors or pavilion roofs that feature uncommon footprints like heptagons (7-sided) or decagons (10-sided) utilizing the central angles and apothems.
Frequently Asked Questions
Does this work for 'Irregular' Polygons?
No. This calculator is strictly for Regular Polygons—shapes where every single side is the exact same length, and every internal angle is the exact same degree. Irregular polygons cannot be solved with a single side length; they require coordinate geometry (like the Shoelace formula).
What is the difference between an Inradius and Circumradius?
The Inradius (Apothem) is the radius of the largest circle that can fit completely inside the polygon (touching the flat sides). The Circumradius is the radius of the circle that fits completely outside the polygon (touching every pointy vertex).
How accurate is this calculator?
Our calculator uses industry-standard formulas to provide the most accurate results possible. However, it should be used for informational purposes only and not as a basis for formal calculations or legal advice.