Calculate angles and properties of convex polygons.
Polygon Geometry
Polygon Properties
720°
Sum of Interior Angles
Calculated geometric properties based on the number of sides.
Each Interior Angle120.00°
Each Exterior Angle60.00°
Area (Regular)259.81
About this calculator
Quick Reference
n = 3Triangle
n = 4Quadrilateral
n = 5Pentagon
n = 6Hexagon
n = 8Octagon
n = 10Decagon
Defining Convexity
A polygon is convex if all its interior angles are less than 180 degrees. This means that no 'dents' point inward, and any line segment between two points inside the polygon stays entirely within the polygon.
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Pro Tips
The sum of exterior angles for ANY convex polygon is always exactly 360°.
A regular polygon has all sides and all angles equal.
As n increases, the polygon looks more and more like a circle.
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Fun Facts
"Bees use hexagonal cells (n=6) because they are the most efficient way to tile a surface with the least wax."
"In some parts of the world, stop signs are octagons (n=8)."
"Triangles (n=3) are the only polygons that are always convex."
