Regular polygon area calculator
Calculate the area, perimeter and apothem of a regular polygon using its number of sides and side length.
Enter an integer side count from 3 to 10,000 and a positive side length. All sides and angles must be equal.
Result
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How to use this calculator
Enter an integer side count from 3 to 10,000 and a positive side length. All sides and angles must be equal.
Formula and method
Apothem a=s/[2 tan(π/n)], perimeter P=n×s and area A=P×a/2. The angle π/n is in radians.
Worked example
A square (n=4) with side 3 has apothem 1.5, perimeter 12 and area 9 square units.
Limits and interpretation
This requires a convex regular polygon, not an irregular or star polygon. Use consistent units for every length.
Frequently asked questions
How should I interpret the result?
A square (n=4) with side 3 has apothem 1.5, perimeter 12 and area 9 square units.
What inputs and assumptions are required?
This requires a convex regular polygon, not an irregular or star polygon. Use consistent units for every length.