Calculate how many spheres can fit inside a container with our Sphere Packing Calculator. Estimate theoretical and practical packing, and calculate costs in multiple currencies.
Your Summary
Packing Results
| Metric | Value |
|---|---|
| Container Volume | |
| Single Sphere Volume | |
| Theoretical Spheres (FCC/HCP Packing) | |
| Practical Spheres (Random Packing) | |
| Total Cost (Theoretical) | |
| Total Cost (Practical) |
Understanding Sphere Packing and Costs
What is Sphere Packing? Sphere packing involves arranging spheres in a container to maximize the number that can fit. The densest arrangement (FCC or HCP) achieves a packing efficiency of ~74%, but practical packing often reaches only ~64% due to random arrangements and boundary effects.
Cost Considerations:
- The cost is calculated based on the number of spheres and the cost per sphere in your selected currency.
- Exchange rates are approximate and may vary. Rates used: 1 EUR = 1.05 USD, 1 GBP = 1.25 USD, 1 INR = 0.012 USD.
Applications:
- Science: Models the arrangement of atoms in crystals (e.g., metals).
- Engineering: Used in material science for designing composites or porous materials.
- Logistics: Helps optimize packing of spherical objects (e.g., fruits, balls) in containers and estimate costs.
Limitations: These calculations assume uniform spheres and a large container relative to the sphere size. In practice, boundary effects, sphere size variations, and packing method (e.g., shaking vs. pouring) can affect the actual number of spheres that fit. Costs are estimates based on approximate exchange rates.
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