Polygon Area Calculator - Free Online Regular Polygon Calculator
Regular Polygon Area Calculator
Calculate the area, perimeter, and properties of regular polygons. Choose from common shapes or enter a custom number of sides.
Select Polygon Type
Polygon Properties
Number of sides:
How to use this calculator
📐 How to Use the Polygon Area Calculator
- Select a polygon type from the preset shapes or enter a custom number of sides
- Enter the length of one side (all sides are equal in regular polygons)
- Choose your preferred unit of measurement
- Click "Calculate Polygon Properties" to see all measurements
- View the visual representation and comprehensive results
📏 Regular Polygon Formulas
Area Formula:
A = (n × s² × cot(π/n)) / 4
Where n = number of sides, s = side length
Apothem (center to side):
a = s / (2 × tan(π/n))
Interior Angle:
θ = (n - 2) × 180° / n
🌟 Common Regular Polygons
Triangle (3 sides)
Interior angle: 60°, Used in trusses and stability
Square (4 sides)
Interior angle: 90°, Most common in construction
Pentagon (5 sides)
Interior angle: 108°, Pentagon building, home plate
Hexagon (6 sides)
Interior angle: 120°, Honeycombs, bolts, tiles
Octagon (8 sides)
Interior angle: 135°, Stop signs, gazebos
Dodecagon (12 sides)
Interior angle: 150°, Clock faces, coins
💡 Pro Tips
- • Regular polygons have all sides equal and all angles equal
- • As the number of sides increases, the polygon approaches a circle
- • Hexagons are the most efficient for tiling (no gaps)
- • The apothem is the perpendicular distance from center to any side
- • The circumradius connects the center to any vertex
- • Only triangles, squares, and hexagons can tile a plane without gaps
⚠️ Common Mistakes to Avoid
- • These formulas only work for REGULAR polygons (equal sides and angles)
- • Don't confuse apothem with radius - apothem is always shorter
- • Interior angles add up to (n-2)×180°, not n×180°
- • Area increases with the square of the side length
- • Make sure your calculator is in the correct mode (degrees vs radians)
About this calculator
Calculate area and perimeter of regular polygons (pentagon, hexagon, octagon, etc.). Free calculator with visual diagrams and formulas.
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