Geometry Circle 360 Degrees Calculator Interactive

This interactive 360-degree circle calculator helps you explore geometry concepts with visual results. Whether you're studying angles, arcs, or circumferences, this tool provides instant calculations and clear explanations.

Introduction

A circle is a fundamental geometric shape where all points on the edge are equidistant from the center. The full circle measures 360 degrees, which is the basis for all circular measurements. This calculator allows you to explore various circle properties interactively.

Key circle properties include radius, diameter, circumference, and central angles. Understanding these relationships is essential for geometry, engineering, and many practical applications.

How to Use This Calculator

Enter the radius of your circle in the input field
Select the units (centimeters, meters, inches, etc.)
Click "Calculate" to see the results
View the visual representation of your circle
Use the "Reset" button to clear all values

Circle Basics

The circle is defined by its center point and radius. Key elements include:

Radius (r): Distance from center to edge
Diameter (d): Twice the radius (d = 2r)
Circumference (C): Distance around the circle
Central angle: Angle formed by two radii
Arc length: Portion of circumference

Key Formulas

Circumference: C = 2πr

Area: A = πr²

Arc Length: L = (θ/360) × 2πr

Sector Area: A = (θ/360) × πr²

Worked Examples

Example 1: Basic Circle Properties

Given a circle with radius 5 cm:

Diameter = 2 × 5 cm = 10 cm
Circumference = 2 × π × 5 ≈ 31.42 cm
Area = π × 5² ≈ 78.54 cm²

Example 2: Arc Length Calculation

For a 90-degree arc in a circle with radius 10 cm:

Arc length = (90/360) × 2 × π × 10 ≈ 15.71 cm

Frequently Asked Questions

What is the difference between a circle and a sphere?

A circle is a two-dimensional shape, while a sphere is its three-dimensional counterpart. Both have constant curvature.

How do I convert degrees to radians?

Multiply degrees by π/180 to convert to radians. For example, 180° = π radians.

What's the smallest angle in a circle?

The smallest meaningful angle is 1 degree, which is 1/360 of a full circle.