# Sizewise How Many Fit

> How many Earths fit in the Sun, golf balls in a room or pallets in a trailer? Counts how many of one thing fit in another by length, by area, by volume (with the packing fractions of real spheres) or as whole boxes stacked in layers, using Wikidata sizes or your own dimensions.

Part of usefulweb.app (https://usefulweb.app/). Part of [Sizewise](https://sizewise.usefulweb.app/) (ownerApp: sizewise). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://sizewisefitcount.usefulweb.app/ (interactive tool at https://sizewisefitcount.usefulweb.app/tool)
- JSON API: POST https://sizewisefitcount.usefulweb.app/api/v1/calculate with a JSON object of inputs (schema: https://sizewisefitcount.usefulweb.app/api/v1/tool)
- OpenAPI: https://sizewisefitcount.usefulweb.app/openapi.json
- MCP (Streamable HTTP): https://sizewisefitcount.usefulweb.app/mcp - tool `sizewise_fit_count`

## Inputs
- item (text): What to fit - An object from the list, or your own: “Box = 40 × 30 × 20 cm”, “Ball = ⌀ 22 cm” or “Rope = 12 m”.
- container (text): Where to fit it - Same choices as above, for example “Room = 5 × 4 × 2.5 m”.
- mode (select): Count by
- packing (select): Gaps between round things
- keepUpright (boolean): Keep boxes upright - Whole boxes only: the third dimension stays vertical (pallets, fridges).

## Method
- Length: the container’s longest known dimension divided by the item’s. Area: rectangles from two dimensions or the cross-section of a round object (π d² ÷ 4). Volume: boxes from three dimensions, spheres from the diameter (π d³ ÷ 6).
- Round items lose space to gaps: equal spheres fill at most π ÷ (3√2) ≈ 74.05 % (Kepler conjecture, proved by Hales), about 64 % when poured at random (random close packing); circles in a plane at most π ÷ (2√3) ≈ 90.69 %.
- Whole boxes: for each choice of the upright side, the floor is filled with rows in up to two orientations (all splits tried), and the layers are stacked; the best total wins. Mixed patterns beyond two row orientations are not searched, so the count is a guaranteed lower bound.

## Limits
- Real objects are not perfect spheres or boxes; the counts are geometric. Planets and stars are treated as spheres of their mean or equatorial diameter.