Sphere Packing Helper

Sphere Packing Helper is a compact tool for estimating how many equal-size spheres fit inside a rectangular box. It is built for students, makers, and planners who want a quick, readable answer without spreadsheets. Type the box dimensions, set one sphere diameter, adjust the packing coefficient, and the app returns an approximate count with helpful notes. No sign-in, no accounts, and no background data—just a focused calculator with a few reference screens.

HOW IT WORKS
• Box: enter Length, Width, Height (use the same unit everywhere).
• Sphere: enter one diameter; the model assumes identical balls.
• Packing coefficient (α): choose how tightly spheres can be arranged. About 0.74 represents hexagonal close packing, ~0.64 represents random close packing; smaller values reflect looser layouts. A caption lists common ranges.
• Formula: N ≈ α × (box volume ÷ sphere volume). A reminder explains that real walls, corners, and tolerances reduce the ideal count.

WHAT’S INSIDE
• Calculator with inputs, slider, and a clear result label.
• Presets such as a ball pit, a tennis-ball box, and a car trunk—use one as a starting point.
• Encyclopedia with short pages on packing science, limits near 74%, and boundary effects.
• Intuition Test with quick multiple-choice questions and instant feedback.
• History that stores recent calculations so you can reuse dimensions later.
• About with a short overview of goals and defaults.

PRACTICAL TIPS
Measure the open interior of the container. If corners are rounded or there are dividers, reduce α slightly. For quick estimates pick 0.64; for careful stacking move toward 0.74. Because volume scales with the cube of diameter, even a tiny change in sphere size can shift the result a lot. When spheres compress or inflate, treat the diameter as the largest expected size.

WHY THIS APP
Sphere packing appears in everyday tasks: filling vases with marbles, loading sports balls, planning bearings in a drawer, estimating beads for crafts, or approximating how many foam peanuts fit in a box. Many sources explain the theory but do not include a simple calculator. This app keeps the math transparent, exposes the one assumption that matters (α), and lets you explore what-ifs in seconds. The output is not a certification; it is a consistent, repeatable estimate that makes planning, comparing options, and communicating decisions easier.

DESIGN NOTES
The layout favors legibility: large inputs, a gentle slider, friendly labels, and concise tooltips. Bright-on-dark colors reduce glare, and buttons respond instantly. Once installed the app works offline; the calculator, history, encyclopedia, and quiz do not require a connection. WebView is used only to display this privacy policy so that the text renders the same on every device.

LIMITATIONS
The model assumes perfect spheres and a rectangular interior; it does not simulate friction or exact layer patterns. Small containers magnify boundary losses while big containers reduce them. Treat results as planning guidance and verify with real objects when precision matters.

ROADMAP
Planned improvements include on-screen unit switching, more presets, optional export of history to a text file, and small diagrams that show how α changes the count. Suggestions are welcome and are prioritized for clarity, usefulness, and ease of implementation.

SUMMARY
Enter dimensions, set diameter, pick a coefficient, and tap Calculate. With presets, a brief encyclopedia, a minute-long quiz, and a handy history, Sphere Packing Helper turns a niche question into a straightforward, learnable routine you can trust from project to project.