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Regular Polygon Area Calculator

Find the area and perimeter of a regular polygon.

Result

259.81
60.00

How it is calculated

For a regular polygon with n equal sides of length s the tool uses A = n × s² / (4 × tan(π / n)) and P = n × s. The angle π / n is in radians. The number of sides must be a whole number of at least 3 (a value like 5.5 is rejected), and the side length must be positive. Area comes out in the square of the unit you used for the side and the perimeter in the same unit as the side; the tool shows plain numbers with two decimals. The formula is only valid when every side and every angle are equal, so it does not work for irregular shapes.

Worked example

Take a regular hexagon with side 10. tan(π / 6) = tan 30° ≈ 0.57735. Numerator: 6 × 10² = 600. Denominator: 4 × 0.57735 = 2.3094. Area = 600 / 2.3094 = 259.81 square units. Perimeter = 6 × 10 = 60.00 units.

Try this example →

Common mistakes

  • Using the formula for a shape whose sides or angles differ; it only holds for regular polygons.
  • Entering the distance from the centre (radius) or the apothem as the side length.
  • Counting the sides wrongly, for example 5 for a hexagon.
  • Mixing units, such as side in centimetres and a result expected in square metres.
  • Entering a fractional number of sides; it must be a whole number of at least 3.

About this calculator

This tool calculates the area and perimeter of a regular polygon — a shape where all sides and all interior angles are equal, like a regular pentagon or hexagon — from just the number of sides and the length of one side. It uses the standard formula that relates a regular polygon's area to its number of sides, side length, and the apothem (the distance from the center to the midpoint of a side), a relationship that generalizes the familiar area formulas for squares and equilateral triangles to any number of sides.

It is used by students verifying geometry homework involving polygons beyond the basic triangle and square cases, and by people in practical design or construction contexts — laying out a hexagonal tile pattern, cutting a pentagonal sign, or estimating material for an octagonal deck or gazebo — who need the area or perimeter of a many-sided shape without deriving the formula from scratch each time.

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