Math

Regular Polygon Calculator

Enter the number of sides and the side length of a regular polygon.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Apothem
Apothem
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Perimeter
—
Area
—
Interior angle (°)
—
Sum of interior angles (°)
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Regular Polygon Calculator by TheCalcTools

How the Regular Polygon Calculator works

Enter the number of equal sides and the length of one side.

The apothem is the distance from the centre to the middle of a side.

Area is half the perimeter times the apothem.

The formula

Area = n s² ÷ (4 tan(π ÷ n))Interior angle = (n − 2) × 180° ÷ n

Worked example

Using the default values shown in the calculator:

Number of sides (n)6
Side length (s)4
  1. For a hexagon with side 4: interior angle = (6 − 2) × 180 ÷ 6 = 120°.
  2. Apothem = 4 ÷ (2 × tan 30°) = 3.4641.
  3. Area = 6 × 16 ÷ (4 × tan 30°) = 41.5692.

Result:

Apothem3.4641
Perimeter24.0000
Area41.5692
Interior angle (°)120.00
Sum of interior angles (°)720

Frequently asked questions

What makes a polygon regular?

All sides have equal length and all interior angles are equal.

What is the interior angle of a hexagon?

120°. (6 − 2) × 180 ÷ 6 = 120.

Sources and further reading

Triangle Area Calculator (Heron's Formula)Enter three side lengths to find the triangle's area, perimeter and angles Circle CalculatorEnter the radius to get the diameter, circumference and area of a circle Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)Choose what you know and enter the values Pythagorean Theorem CalculatorSolve for any side of a right triangle using a² + b² = c² Rectangle CalculatorEnter the length and width to find the area, perimeter and diagonal Trapezoid Area CalculatorEnter the two parallel sides and the height to find the area of a trapezoid

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