Sizewise How Many Fit

What it is for

"How many Earths fit in the Sun?" and "How many pallets fit on this trailer?" are the same question at very different scales. How Many Fit answers both. It takes an item and a container — from the Sizewise library or your own entries — and counts in one of four ways: length (end to end), area, volume or whole boxes in layers.

Pure ratios are the classic answer to trivia questions. Real objects leave gaps, so the tool can also apply the packing fraction of spheres, and for boxes it finds an actual arrangement of rows on the floor, layer by layer.

It is not a load planner: it ignores weight limits, axle loads, doors and mixed cargo, and it tries rows in at most two orientations per layer.

Worked example

The first example asks how many Earths fit in the Sun by volume. The answer is 1 302 096 × Earth fit in Sun by volume — the cube of the diameter ratio (1,391,400 km against 12,742 km). NASA quotes "about 1.3 million", so the numbers agree.

That count assumes you could melt the Earths and pour them in. Choose Gaps between round things: densest and the count falls to 74.05 % of it, the best equal spheres can do (the Kepler conjecture, proved by Thomas Hales).

The second example packs Pallet load = 1.2 × 0.8 × 1.6 m into Trailer = 13.6 × 2.48 × 2.7 m as whole boxes with Keep boxes upright on. Result: 34 × Pallet load fit in Trailer (34 per layer, 1 layer). The metrics show an exact volume ratio of 59.29, but only one 1.6 m layer fits under 2.7 m, and the note says 57.3 % of the space is used. The floor plan shows two rows of 17 pallets, 1.2 m across each.

The third example pours golf balls into a cubic metre: the volume ratio is 24,583, and with random packing (64 %) you get 15,733 balls.

How to read the result

• Count is the whole number of items. For ratios it is rounded down.
• Exact ratio is the pure size ratio before gaps or rounding — useful to see how much a packing costs.
• Packing fraction is 1 for pure ratios and boxes, 0.7405 for densest sphere packing and 0.64 for random packing.
• Layers and Per layer appear for whole boxes. The SVG shows one layer from above.
• Notes state the assumptions, for example which side stays upright and how much space is used.

Tips and common mistakes

• Enter boxes as Name = 40 × 30 × 20 cm, balls as Ball = ⌀ 22 cm and lines as Rope = 12 m.
• Volume needs three dimensions or a round object. Many library objects only have one size; the tool says so instead of guessing (an Olympic pool, for example, has no depth in the data).
• Turn on Keep boxes upright for pallets, fridges and anything with a "this way up" arrow; otherwise boxes may be tipped onto their sides if that fits more.
• The box count is a guaranteed minimum. Clever mixed patterns sometimes fit one or two more.
• Swap item and container to ask the question the other way round.

FAQ

Why is the box count lower than the volume ratio?

Whole boxes cannot be cut, and leftover strips along the walls and above the top layer stay empty.

What does 64 % packing mean?

Spheres poured into a container settle into a random arrangement that fills about 64 % of the space (random close packing, Scott and Kilgour 1969).

Can I count flat things like tiles?

Yes, use Area with two dimensions, for example Tile = 30 × 30 cm in Floor = 4 × 3 m.

Does it work in the app too?

Yes, the How many fit view in Sizewise uses the same engine.