Polygon Exterior Angles Calculator | Real-Time Geometry Tool

Polygon Parameters

Number of Sides (3-100)

Drag the slider or enter a value (3 for triangle, 4 for square, etc.)

Polygon Type

Angle Units

Degrees (°) Radians (rad) Gradians (gon)

Quick Polygon Selection

Calculation Precision

Actions

Real-Time Results

Exterior Angle

60.00

degrees (°)

Each Angle

Interior Angle

120.00

degrees (°)

Supplementary

Sum of Exterior Angles

360.00

degrees (°)

Always Constant

Sum of Interior Angles

720.00

degrees (°)

Formula: (n-2)×180°

Key Insight: The sum of exterior angles of any polygon is always 360°, regardless of the number of sides. Each exterior angle = 360° / n (where n is the number of sides).

Visualization & Features

Polygon Visualization

Number of Sides: 6 Shape: Hexagon

Angle Calculation Formula

Exterior Angle Formula: E = 360° / n

Interior Angle Formula: I = 180° - E

Sum of Interior Angles: S_I = (n - 2) × 180°

Sum of Exterior Angles: S_E = 360° (always)

Where n = number of sides

Calculation History

Tool Features

Real-Time Calculation

Visual Polygon Display

Calculation History

Multiple Units

Understanding Polygon Exterior Angles: A Complete Guide

This comprehensive guide will help you understand exterior angles of polygons, how to calculate them, and why this knowledge is essential in geometry, architecture, and design.

What Are Exterior Angles of a Polygon?

An exterior angle of a polygon is formed by extending one of its sides and measuring the angle between this extension and the adjacent side. For any polygon, whether regular or irregular, the sum of all exterior angles is always 360 degrees.

How to Calculate Exterior Angles

For a regular polygon (where all sides and angles are equal), calculating exterior angles is straightforward:

Formula: Exterior Angle = 360° ÷ Number of Sides
Example for a hexagon (6 sides): 360° ÷ 6 = 60° per exterior angle
The interior angle is supplementary to the exterior angle: Interior Angle = 180° - Exterior Angle

Real-World Applications

Understanding polygon exterior angles has practical applications in various fields:

Architecture & Design: Creating symmetrical structures, tiling patterns, and aesthetic layouts
Engineering: Designing mechanical parts, gear teeth, and structural components
Computer Graphics: Rendering 3D models, game development, and CAD software
Surveying & Land Mapping: Calculating property boundaries and land divisions

Using This Polygon Exterior Angles Calculator

Our tool provides instant, accurate calculations for any polygon from 3 to 100 sides:

Adjust the number of sides using the slider or input field
Select polygon type (regular or irregular)
Choose your preferred angle units (degrees, radians, or gradians)
View real-time results with visual representation
Use the history feature to track previous calculations

Important Note

While the exterior angle formula works perfectly for regular polygons, irregular polygons have varying exterior angles. However, the sum of all exterior angles still equals 360° for any polygon, regardless of regularity.

This polygon exterior angles calculator is an essential tool for students, teachers, architects, designers, and anyone working with geometric shapes. Bookmark this page for quick access to accurate polygon calculations anytime!

Advanced Features of Our Polygon Calculator

Real-Time Updates

See results instantly as you adjust parameters

Visual Polygon Render

Interactive visualization of calculated polygon

Multi-Unit Support

Calculate in degrees, radians, or gradians

Calculation History

Track and recall previous calculations