Round Bin Capacity

A round bin is a cylinder, and its volume is the area of the floor times the depth of grain. Everything difficult about this calculation is in the units and in which dimensions get measured.

The bushel conversion is pure geometry and worth deriving once. A US bushel is defined as exactly 2,150.42 cubic inches, and a cubic foot is 1,728 cubic inches, so one cubic foot holds 1,728 ÷ 2,150.42 = 0.8036 bushels, and one bushel occupies 1.2445 ft³. Folding that into the cylinder gives the rule of thumb that grain handlers actually use: bushels ≈ 0.6311 × diameter² × depth, with both dimensions in feet, because $\pi/4 \times 0.8036 = 0.6311$. An 18 ft bin holding 20 ft of grain is $0.6311 \times 324 \times 20 \approx 4{,}090$ bushels. In metric the same rule is simply $0.7854 \, d^2 h$ for cubic metres.

Two measurement habits cause nearly all the errors. The first is using the bin's height instead of the depth of grain — a bin is almost never full to the eave, and the number wanted is the level fill. The second is taking the outside diameter of a corrugated wall; the inside diameter is what holds grain, and on an 18 ft bin the corrugation is worth an inch or two, which is under 2%. Neither of these is as large as the third omission: the peaked cone above a level fill, which on a wide bin can be several hundred bushels and needs its own calculation rather than a fudge factor on this one.

The deeper caution is that this is a volume, and grain is traded by weight. A bushel in a sales contract is a legal mass — 60 lb of wheat, 56 lb of corn — not a volume of grain, and converting bin volume to saleable quantity needs the crop's bulk density. Nor is a bin's contents constant over the winter: grain settles and packs under its own weight, and a deep bin holds several percent more than the unpacked calculation suggests, which is why commercial capacity tables include a packing factor that rises with depth. For inventory work that factor matters; for sizing and aeration it does not.