Calculator

Free Online Polygon Calculator: Area, Perimeter & Angles

Free Online Polygon Calculator: Area, Perimeter & Angles

Polygon Formulas Explained: How to Calculate Area and Interior Angles

Number of Sides (n): Side Length (a):

What is Plane Polygon Calculator?

A Plane Polygon Calculator quickly finds the area, perimeter, and angles of any regular polygon using only the number of sides and side length. It handles polygons like triangles, pentagons, hexagons, and beyond, up to 1000 sides.

With this tool, you instantly get precise results and step-by-step formulas, making it ideal for students, teachers, and exam preparation. It works on mobiles and desktops, no extra apps or logins needed.

Formula Behind Plane Polygon Calculator

This calculator uses these proven formulas: Perimeter = n × a (number of sides × side length); Area = [n × a²] / [4 × tan(π/n)]; Each Interior Angle = [(n−2) × 180°] / n; and Sum of Interior Angles = (n−2) × 180°. These apply to regular polygons in plane geometry, ensuring accurate and consistent results every time.

Polygon Calculation Table (Common Examples)

Polygon Name	Sides (n)	Side (a)	Area	Perimeter	Each Angle (°)
Equilateral Triangle	3	4	6.9282	12	60.00
Square	4	4	16.0000	16	90.00
Pentagon	5	4	27.5276	20	108.00
Hexagon	6	4	41.5692	24	120.00
Octagon	8	4	77.2548	32	135.00

Steps to Use Polygon Calculator

Enter the number of sides (minimum 3).
Enter the side length in your chosen unit.
Click "Calculate".
Get instant results for area, perimeter, and angles with worked-out steps.

Why Use Vedantu’s Plane Polygon Calculator?

This tool delivers instant, reliable answers with formula breakdowns for all regular polygons. Whether for homework, teaching, or quick revision, you get visually clear steps, not just final answers.

Optimized for any device, it gives you complete transparency—no guesswork, no calculation errors. Plus, its logic is aligned with CBSE, NCERT, and major board practices, reviewed by expert educators.

Applications of Plane Polygon Calculators

Polygon geometry calculators are a go-to in architecture (for tiling, floor plans), engineering (panel design), mathematics, and even robotics. They’re invaluable for students tackling geometry problems and competitive exams.

In art, mosaics, nature (honeycomb hexagons), and daily life objects, you’ll find polygons everywhere. You can also use this calculator to forward-check polygon properties when customizing geometric figures for projects or contests.

For more maths and geometry support, check tools like the HCF Calculator, Prime Numbers, and essential lessons on Algebra Topics.

Related reading for deeper understanding: Types of Polygons and Area of Polygon Derivations.

FAQs on Free Online Polygon Calculator: Area, Perimeter & Angles

1. What is a polygon in geometry?

A polygon is a closed two-dimensional figure formed by connecting three or more straight line segments. These segments are called sides, and the points where they meet are called vertices. Polygons are classified based on the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and so on.

2. How do I calculate the perimeter of a polygon?

The perimeter of a polygon is the total length of all its sides. For a regular polygon (where all sides are equal), you simply multiply the length of one side by the number of sides. For irregular polygons, you need to add up the lengths of all the individual sides.

3. What is the formula for the area of a polygon?

There isn't one single formula for the area of all polygons. The formula varies depending on the type of polygon. For example, the area of a triangle is (1/2) * base * height, while the area of a rectangle is length * width. More complex polygons require more advanced formulas or methods like dividing them into smaller, simpler shapes.

4. What is a regular polygon?

A regular polygon is a polygon where all sides are equal in length and all angles are equal in measure. Examples include equilateral triangles, squares, and regular pentagons. Regular polygons have symmetrical properties and are often used in geometric constructions.

5. How do you find the sum of interior angles of a polygon?

The sum of the interior angles of a polygon with 'n' sides is given by the formula (n - 2) * 180°. For example, a triangle (n=3) has a sum of interior angles of (3-2)*180° = 180°, while a quadrilateral (n=4) has (4-2)*180° = 360°.

6. What are some different types of polygons?

Polygons are categorized based on the number of sides: triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), heptagons (7 sides), octagons (8 sides), and so on. They can also be classified as regular (all sides and angles equal) or irregular (sides and/or angles unequal), convex (all interior angles less than 180°), or concave (at least one interior angle greater than 180°).

7. How can I calculate the area of a regular hexagon?

The area of a regular hexagon with side length 'a' can be calculated using the formula: Area = (3√3/2) * a². This formula is derived by dividing the hexagon into six equilateral triangles.

8. What are the interior angles of a regular pentagon?

Each interior angle of a regular pentagon measures 108°. This is calculated using the formula for the sum of interior angles ((n-2) * 180°), where n=5, and then dividing by the number of angles (5).

9. What are some real-world examples of polygons?

Polygons are everywhere! Think about the shapes in architecture (buildings, bridges), art (mosaics, stained glass), nature (honeycombs, crystals), and everyday objects (traffic signs, tiles). Many designs and structures utilize polygon shapes for their stability and aesthetic appeal.

10. How do I use a polygon calculator to find the area?

Using a polygon calculator typically involves inputting the necessary information about the polygon, such as the number of sides and the length of each side (or other relevant dimensions depending on the calculator's design). Once the input is entered, the calculator will perform the relevant calculations and display the area (along with other properties, like perimeter and angles, depending on the calculator's features).

11. What's the difference between a convex and concave polygon?

In a convex polygon, all interior angles are less than 180°. If you draw a line segment connecting any two points within a convex polygon, the entire segment will remain inside the polygon. In a concave polygon, at least one interior angle is greater than 180°. A line segment connecting certain points inside a concave polygon would extend outside the shape.