🔷 Polygon Calculator
Calculate properties of regular polygons
Must be 3 or greater
How to Use This Calculator
Enter Number of Sides
Input the number of sides (n) of your regular polygon. Must be 3 or greater (triangle, square, pentagon, hexagon, etc.).
Enter Side Length
Input the length of one side of the regular polygon.
Click Calculate
Press the "Calculate Polygon Properties" button to get all polygon measurements including area, perimeter, angles, and more.
Formulas
Area = (n × s²) / (4 × tan(π/n))
Perimeter = n × s
Interior Angle = (n-2) × 180° / n
Exterior Angle = 360° / n
Where:
- n = Number of sides
- s = Side length
- π ≈ 3.14159
Examples:
Triangle (n=3): Interior Angle = (3-2)×180°/3 = 60°
Square (n=4): Interior Angle = (4-2)×180°/4 = 90°
Pentagon (n=5): Interior Angle = (5-2)×180°/5 = 108°
About Polygon Calculator
The Polygon Calculator helps you find the area, perimeter, angles, and other properties of regular polygons. A regular polygon has all sides equal and all angles equal.
When to Use This Calculator
- Geometry: Calculate polygon properties for geometric problems
- Architecture: Design polygonal structures and calculate dimensions
- Engineering: Design polygonal components and mechanical parts
- Education: Learn and practice polygon mathematics
- Design: Create polygonal patterns, logos, or graphics
- Construction: Plan polygonal structures and estimate materials
Why Use Our Calculator?
- ✅ Universal: Works for any regular polygon (3+ sides)
- ✅ Complete Properties: Calculates area, perimeter, angles, and more
- ✅ Instant Results: Get all measurements immediately
- ✅ Step-by-Step Display: See calculation formulas
- ✅ 100% Accurate: Precise geometric calculations
- ✅ Completely Free: No registration required
Understanding Regular Polygons
A regular polygon is a polygon with all sides equal and all angles equal. Common regular polygons:
- Triangle (n=3): Equilateral triangle
- Square (n=4): Regular quadrilateral
- Pentagon (n=5): Regular five-sided shape
- Hexagon (n=6): Regular six-sided shape (honeycomb)
- Octagon (n=8): Regular eight-sided shape (stop sign)
- Decagon (n=10): Regular ten-sided shape
Real-World Applications
Architecture: Many buildings use polygonal designs. The Pentagon building is a famous example, and many modern buildings incorporate polygonal elements.
Nature: Regular polygons appear in nature - hexagons in honeycombs, pentagons in flowers, triangles in crystal structures.
Design: Polygons are fundamental in graphic design, logo creation, and pattern design. Understanding their properties helps create balanced compositions.
Frequently Asked Questions
What is a regular polygon?
A regular polygon is a polygon where all sides have equal length and all interior angles are equal. Examples include equilateral triangles, squares, regular pentagons, hexagons, etc.
How do you calculate polygon area?
For a regular polygon with n sides and side length s, area = (n × s²) / (4 × tan(π/n)). This formula works by dividing the polygon into n isosceles triangles.
What is the interior angle formula?
Interior angle = (n-2) × 180° / n, where n is the number of sides. For example, a hexagon (n=6) has interior angles of (6-2)×180°/6 = 120°.
What is the exterior angle of a polygon?
Exterior angle = 360° / n. The sum of all exterior angles of any polygon is always 360°, regardless of the number of sides.
Can I use this for irregular polygons?
This calculator is specifically for regular polygons (equal sides and angles). For irregular polygons, you'd need different methods like the shoelace formula or dividing into triangles.
What's the difference between apothem and circumradius?
Apothem is the distance from the center to the midpoint of a side. Circumradius is the distance from the center to a vertex. For regular polygons, circumradius > apothem.
What is the minimum number of sides for a polygon?
The minimum is 3 sides (a triangle). Polygons must have at least 3 straight sides. A two-sided figure would just be a line segment.