What is the formula for the area of a regular polygon?

Given side length s and n sides: A = (n × s²) / (4 × tan(π / n)). Given circumradius R (center to vertex): A = (n × R² × sin(2π / n)) / 2. Both formulas give identical results when the input describes the same polygon.

What is a regular polygon?

A regular polygon has n equal sides and n equal interior angles. Common examples include equilateral triangles (n=3), squares (n=4), pentagons (n=5), hexagons (n=6), and octagons (n=8).

What is the circumradius?

The circumradius R is the distance from the center of the polygon to any of its vertices. It equals s / (2 × sin(π / n)), where s is the side length.

What is the apothem and how does it relate to this calculator?

The apothem a is the perpendicular distance from the center to the midpoint of a side — the inradius. It equals s / (2 × tan(π / n)). The side-length formula used here is equivalent to A = n × a × s / 2.

Does this work for triangles and squares?

Yes. For n=3 it gives the equilateral triangle area. For n=4 it gives the square area (s²). You can verify: entering s=5 for n=4 returns 25, and entering s=5 for n=6 matches the standard hexagon formula.

What units does the result use?

The area is expressed in square units matching your chosen unit. For example, entering 5 cm gives an area in cm².

Area of a Regular Polygon Calculator

Name: Area of a Regular Polygon Calculator
Availability: InStock
Author: Nham Vu

Enter the number of sides and side length (or circumradius) to instantly calculate the area of any regular polygon with step-by-step working.

Polygon Dimensions

Number of sides (n)

Calculate from

Side length (s)

Unit

Formulas

A = (n × s²) / (4 × tan(π/n))

From side length s

A = (n × R² × sin(2π/n)) / 2

From circumradius R

Area

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Enter values and click Calculate

Polygon diagram

All sides and interior angles are equal

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Summary

Enter the number of sides and side length (or circumradius) to instantly calculate the area of any regular polygon with step-by-step working.

How it works

Choose the number of sides of your regular polygon (3 to 100).
Select whether you are entering the side length or the circumradius.
Type the measurement value in the input field.
Choose a unit from the dropdown (mm, cm, m, in, ft).
Click "Calculate Area" to apply the correct formula.
The result and a full step-by-step breakdown appear on the right.

Use cases

Geometry homework involving triangles, pentagons, hexagons, and beyond.
Architecture and design using regular polygon floor plans or tiles.
Engineering drawings with bolt, nut, or socket cross-sections.
Game development requiring polygon grid or map cell calculations.
Land surveying with regular-shaped plots.
Teaching the general regular polygon area formula in the classroom.
Verifying manual polygon area calculations quickly.
Comparing areas of polygons with the same perimeter or circumradius.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu