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Carton count is the internal dimensions divided by the carton dimensions, floored in each axis. Rotating the carton often improves the fit substantially, so trying both orientations is worthwhile — a few millimetres can add a whole row.
Container loading
cartons = floor(L/cl) x floor(W/cw) x floor(H/ch) using internal container dimensions
Flooring the division discards the remainder in each axis. A carton 5 mm narrower might fit six across instead of five, adding 20% capacity.
It adds about 13% volume for a small freight premium, so for volume-limited cargo it is almost always the cheaper option per cubic metre.