Regular polygon area calculator

Calculate the area, perimeter and apothem of a regular polygon using its number of sides and side length.

Result

From triangle to polygon

Try 3, 4, 5, 6, 8 or 12 sides at a fixed side length: the shape and result change together. Reveal the triangles to see the division.

How do you calculate regular polygon area?

Divide the shape into one equal triangle per side. Multiply perimeter by apothem and halve it. The apothem follows from the side length and half the central angle.

A = \frac{n \times s^{2}}{4 \times \tan (\frac{π}{n})}

How to use the calculator

Enter measurements with a decimal point or comma: results update immediately. Input units apply to every length; changing them converts the measurements. Changing result units leaves the shape unchanged. The control below the drawing reveals or hides its visual explanation. Copy results includes valid measurements and the result. Reset and Try this example restore the initial values and centimetre units.

The first formula shows the relationship; the second substitutes measurements converted to the result unit. The ≈ sign indicates rounding, including in the substituted values.

A pentagonal plate

Five 4 cm sides give a 20 cm perimeter and about 27.53 cm² of area. The sides and angles must all be equal.

From measurements to the result

Input: $s = 4 cm; n = 5$
Result: $≈ 27.53 {cm}^{2}$

Calculation steps

Calculate the pentagon’s perimeter.
$P = 5 \times 4 = 20$
Complete the calculation using the tool’s formula.
$A = \frac{20 \times 4}{4 \times \tan (\frac{π}{5})}$

Units and interpretation

Area uses square units: 1 m² = 10,000 cm².

Use 3 to 10,000 whole sides, each between 10⁻¹² and 10¹² in the selected unit. Above 120 sides the sketch is schematic; the formula still uses the entered count.

Precision and numerical limits

Lengths range from 0 to 10¹² in the selected unit; triangle sides must be strictly positive. Results use two decimal places, with scientific notation for very small or large values. Calculations use browser precision: unrepresentable positive values produce an error. A rejected unit change keeps the previous data. Calculation takes place in your browser.

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Regular polygon area calculator

Result

From triangle to polygon

How do you calculate regular polygon area?

How to use the calculator

A pentagonal plate

From measurements to the result

Calculation steps

Units and interpretation

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