Circle Packing Density Calculator

Calculate Circle Packing Density (D)





Formula

The formula to calculate the Circle Packing Density (D) is:

\[ D = \frac{N \times A_c}{A_t} \]

Where:

What is Circle Packing Density?

Circle packing density refers to the proportion of a given area that is occupied by circles when they are packed together as closely as possible. This concept is often used in various fields such as material science, logistics, and mathematics to optimize space and resource utilization. The density is a measure of how efficiently the circles fill the container area, and it is expressed as a ratio or percentage. Higher density values indicate more efficient packing, while lower values suggest that there is more unused space within the container.

Example

Let's say the number of circles (N) is 10, the area of one circle (A_c) is 3 square units, and the area of the container (A_t) is 50 square units. Using the formula:

\[ D = \frac{10 \times 3}{50} = 0.6 \]

So, the circle packing density (D) is 0.6 or 60%.

Extended information about "Circle-Packing-Density-Calculator"

How to Calculate Packing Density

Formula: \( \eta = \frac{V_{packed}}{V_{total}} \)

Example: \( \eta = \frac{500}{1000} \)

Linear Packing Density Formula

Formula: \( \eta = \frac{L_{packed}}{L_{total}} \)

Example: \( \eta = \frac{30}{50} \)

Density of a Circle

Formula: \( \rho = \frac{m}{A} \)

Example: \( \rho = \frac{10}{3.14} \)

Packing Density of Spheres

Formula: \( \eta = \frac{\pi}{3\sqrt{2}} \)

Example: \( \eta = \frac{3.14}{3\sqrt{2}} \)

Packing Density vs Bulk Density

Formula: \( \eta = \frac{\rho_{packed}}{\rho_{bulk}} \)

Example: \( \eta = \frac{2.5}{1.2} \)

Circle Packing in Rectangle Calculator

Formula: \( \eta = \frac{n \cdot A_{circle}}{A_{rectangle}} \)

Example: \( \eta = \frac{5 \cdot 3.14}{20} \)

Packing Efficiency of Circles

Formula: \( \eta = \frac{A_{packed}}{A_{total}} \)

Example: \( \eta = \frac{15}{25} \)