Circle Packing Calculator

Calculate optimal circle packing arrangements, packing density, and visualize circle configurations.

Packing Configuration

Container Properties

Visualization

About Circle Packing

What is Circle Packing?

Circle packing is the study of arranging circles in a given space to maximize density or minimize wasted space. It has applications in materials science, computer graphics, facility location, and mathematical optimization.

Packing Types

Container Packing

Pack circles within a bounded container (circle, square, or rectangle). Useful for storage optimization and space planning.

Infinite Packing

Arrange circles in infinite patterns. Hexagonal packing achieves the optimal density of π/(2√3) ≈ 90.69%.

Custom Arrangement

Analyze existing circle arrangements or test specific configurations for density and overlap detection.

How to Use This Calculator

  1. Select your packing type (container, infinite, or custom)
  2. Configure the parameters (container size, circle radius, etc.)
  3. Click "Generate Packing" to visualize the arrangement
  4. Click "Calculate Packing" to get detailed analysis
  5. View density, efficiency, and optimization results

Key Concepts

  • Packing Density: Ratio of area covered by circles to total area
  • Hexagonal Packing: Optimal infinite packing pattern
  • Kissing Number: Maximum number of circles that can touch a given circle
  • Packing Efficiency: How close the arrangement is to theoretical optimum

Applications

  • Materials Science: Atomic arrangements in crystals
  • Manufacturing: Optimal cutting patterns for circular parts
  • Computer Graphics: Procedural texture generation
  • Facility Planning: Optimal placement of circular objects
  • Art and Design: Aesthetic pattern creation

Example Configurations

Try These Examples:

  • 7 circles of radius 1 in a circular container of radius 3
  • Hexagonal packing with circle radius 1 (density ≈ 90.69%)
  • Custom arrangement: 0,0,1 | 2.5,0,1 | 1.25,2.17,1 (equilateral triangle)