Regular Polygon Calculator

Comprehensively calculate the area, perimeter, interior angles, and exterior angles of regular polygons from equilateral triangles to icosagons. Just enter the number of sides and side length.

Results

Polygon Name

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Area

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Perimeter

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Interior Angle

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Exterior Angle

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Central Angle

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Apothem

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Circumradius

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GUIDE

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Automatically Calculate All Regular Polygon Values

A regular polygon is a shape where all sides and interior angles are equal. This calculator automatically calculates area, perimeter, interior angle, exterior angle, and central angle by just entering the number of sides (3-20) and side length. Supports various regular polygons from equilateral triangles to icosagons.

Using Mathematically Accurate Formulas

Area is calculated using the formula (n × s²) / (4 × tan(π/n)), interior angle as (n-2) × 180° / n, and exterior angle as 360° / n. Provides precise results using trigonometric functions.

Essential Tool for Architecture and Design

Regular polygons are frequently used in architecture and interior design, such as hexagonal tiles, octagonal windows, and pentagonal decorations. Calculate accurate area and perimeter for material purchasing and construction planning.

Easy to Understand with Visual Diagrams

Visually displays the shape of the regular polygon with SVG diagrams. The shape is automatically drawn according to the number of sides, making it intuitively understandable. Dark mode is also supported.

Optimized for Math Education

Useful for students learning the properties of regular polygons. You can see in real-time how interior and exterior angles change as you vary the number of sides, helping to develop mathematical intuition.

Supports Both Mobile and Desktop

Responsive design allows convenient use on smartphones, tablets, and desktops anywhere. Calculate on-site immediately or use as educational material in the classroom.

Frequently asked questions

What formula calculates the area of a regular polygon?

Area = (n × s²) / (4 × tan(π/n)), where n is the number of sides and s is the side length. As n increases, the regular polygon approaches the shape of a circle.

What is the difference between interior and exterior angles?

The interior angle is formed between two adjacent sides inside the shape, while the exterior angle is formed between a side and the extension of its neighboring side. Interior + exterior = 180°, and the exterior angles of any regular polygon always sum to 360°.

How does the interior angle change as the number of sides increases?

Using interior angle = (n-2) × 180° / n, the interior angle grows larger and approaches 180° as n increases. For example, an equilateral triangle has 60°, a hexagon has 120°, and a regular dodecagon has 150°.

What do central angle and circumradius mean?

The central angle is the angle formed at the polygon's center between two adjacent vertices (360°/n), and the circumradius is the distance from the center to each vertex. These values are used when inscribing the polygon in a circle.

How many sides can this calculator handle?

This calculator supports regular polygons from an equilateral triangle (3 sides) up to an icosagon (20 sides). Just enter the number of sides and side length to instantly get area, perimeter, interior angle, exterior angle, central angle, and circumradius.