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The dimensions for the ark given in Genesis are 300 cubits long, 50 cubits wide and 30 cubits high (Genesis 6:15). What is a cubit? A cubit is an ancient unit of measurement, the length of the forearm from the elbow to the longest finger (the term “cubit” comes from the Latin word “cubitum” which means “elbow.” The Hebrew word for “cubit” is “ammah.” As everybody’s arms are different lengths, this unit may seem a bit ambiguous to some, but scholars generally agree that it represents somewhere between 17 and 22 inches (43-56 centimeters). The ancient Egyptian cubit is known to have been 21.888 inches. So, doing the math,

300 x 22 inches = 6,600; 50 x 22 inches = 1,100; 30 x 22 inches = 660
6,600/12 = 550 feet; 1100/12 = 91.7 feet; 660/12 = 55 feet.

Thus, the ark could have been up to 550 feet long, 91.7 feet wide and 55 feet high. These are not unreasonable dimensions. But how much storage space does this amount to? Well, 550 x 91.7 x 55 = 2,773,925 cubic feet. (If we take the smallest measurement of cubit, 17 inches, we end up with 1,278,825 cubic feet). Of course, not all of it would have been free space. The ark had three levels (Genesis 6:16) and a lot of rooms (Genesis 6:14), the walls of which would have taken up space. Nevertheless, it has been calculated that a little more than half (54.75%) of the 2,773,925 cubic feet could store 125,000 sheep-sized animals, leaving over 1.5 million cubic feet of free space.

John Woodmorappe, author of the definitive Noah’s Ark: A Feasibility Study, estimated that only about 15% of the animals on the ark would have been larger than a sheep. This figure does not take into account the possibility that God may have brought Noah “infant” animals, which can be significantly smaller than adult animals.

How many animals were on the ark? Woodmorappe estimates about 16,000 “kinds.” What is a “kind”? The designation of “kind” is thought to be much broader than the designation “species.” Even as there are over 400 dog breeds all belonging to one species (Canis familiaris), so many species can belong to one kind. Some think that the designation “genus” may be somewhat close to the biblical “kind.”

Nevertheless, even if we presume that “kind” is synonymous with “species,” “there are not very many species of mammals, birds, amphibians and reptiles. The leading systematic biologist, Ernst Mayr, gives the number as 17,600. Allowing for two of each species on the ark, plus seven of the few so-called “clean” kinds of animals, plus a reasonable increment for known extinct species, it is obvious that not more than, say, 50,000 animals were on the ark” (Morris, 1987).

Some have estimated that there were as many as 25,000 kinds of animals represented on the ark. This is a high-end estimation. With two of each kind and seven of some, the number of animals would exceed 50,000, though not by very much, relatively speaking. Regardless, whether there were 16,000 or 25,000 kinds of animals, even with two of each and seven of some, scholars agree that there was plenty of room for all of the animals on the ark, plus food and water with room to spare.

http://www.gotquestions.org/Noahs-ark-animals.html