Circle Packing Calculator
Calculate optimal circle packing
Frequently Asked Questions
What is circle packing and when is it used?
Circle packing calculates how to fit the maximum number of circles of a given radius into a container shape. It is used in manufacturing (cutting circular pieces from sheet material), logistics (packing cylindrical items), and computational geometry.
What packing arrangements does the calculator support?
The calculator supports square grid packing and hexagonal (honeycomb) packing. Hexagonal packing is more efficient, achieving approximately 90.69% coverage versus 78.54% for square packing.
How is packing efficiency calculated?
Packing efficiency is the ratio of total circle area to container area, expressed as a percentage. Formula: efficiency = (n × π × r²) / container_area × 100%, where n is the number of circles and r is the circle radius.
Can I pack circles into non-rectangular containers?
The current calculator supports rectangular and circular containers. For rectangular containers, both grid and hexagonal arrangements are calculated. For circular containers, concentric ring packing is used.
What is the densest possible circle packing?
The densest packing of equal circles in an infinite plane is hexagonal packing at π/(2√3) ≈ 90.69% efficiency. This was proven by Thue in 1910 and confirmed by Fejes Tóth in 1940. No arrangement can exceed this density.