A 53-foot dry van is 53 feet long on the outside, but the space inside is smaller. Trailers differ by maker and age, so measure or ask, but a typical newer van is about 52 feet 6 inches (630 inches) long, about 100 inches wide and 108 to 110 inches high inside. The door opening is a little narrower and lower than the box, so a pallet that fits inside still has to fit through the doors. Reefers have thick insulated walls, so they're a few inches narrower and shorter inside.
In the US the common pallet is 48 by 40 inches (the 48 is the length of the boards on top). Loaded straight, the 48-inch side runs along the trailer: two pallets side by side take 80 of the 100 inches, and each row uses 48 inches of length. 630 inches fits 13 rows, so 26 pallets on the floor.
Loaded turned, the 40-inch side runs along the trailer: two side by side take 96 inches of width, and each row uses only 40 inches. That fits 15 rows, so up to 30 pallets, if the pallets are true to size and the walls are smooth. Turned is tight: a damaged pallet, a bulging load or a narrower reefer can make it impossible. Mixing straight and turned pallets row by row is called pinwheeling, and is used to make an odd count fit.
53' van, 48x40 pallets, seen from above
Straight (26): NOSE |48|48|48|48|48|48|48|48|48|48|48|48|48| DOORS 13 rows x 2
Turned (30): NOSE |40|40|40|40|40|40|40|40|40|40|40|40|40|40|40| DOORS 15 rows x 2
Height is the third dimension. Pallets that are built to be stacked can go two high (double stacked) if the two together fit under the ceiling, with a few inches to spare to load them with a forklift. Two 54-inch pallets make 108 inches, which fits most vans; two 60-inch pallets don't.
LTL carriers sell space by linear feet: how much of the trailer's length a shipment uses. A row of two straight pallets uses 4 feet of length, so 10 straight pallets in 5 rows use 20 linear feet. Space is also measured in cube, cubic feet of volume: length × width × height in inches, divided by 1,728. A 53-foot van has roughly 3,900 cubic feet inside, but you can never use all of it, because pallets don't fill every gap.
Practice
How many 48×40 pallets fit on the floor of a typical 53-foot van, loaded straight, two wide?
More info
Quick reference
53' van inside
About 630 in long, 100 in wide, 108-110 in high (check the trailer).
48 × 40
The common US pallet, in inches.
Straight
48 in along the trailer: 13 rows, 26 pallets.
Turned
40 in along the trailer: up to 15 rows, 30 pallets.
Pinwheel
Mixing straight and turned rows to fit an odd count.
Double stack
Two stackable pallets one on top of the other.
Linear feet
Trailer length a shipment uses; a straight row of two is 4 ft.