The Bible does not give the height of this ancient building.

The height of the tower is largely a matter of speculation, but since the tower symbolically can be considered a precursor to man's desire to build tall structures throughout history, its height is a significant aspect of its mythos. The historic Tower commissioned by Nebuchadnezzar in about 560 BC in the form of an eight level ziggurat is believed by historians to have been about 100 meters (328 feet) in height. The biblical Tower of Babel however would have been built about 2000 years earlier. The narrative in the book of Genesis does not mention how tall the tower was, and thus it has not been much of a subject of debate among fundamentalist Christians. There are however two extra-canonical sources that mention the tower's height. The Book of Jubilees mentions the tower's height as being 5433 cubits and 2 palms (8,150 feet, 2,484 meters high). This would be approximately four times taller than the world's tallest structures of today and in all of human history. Such a claim would be considered as mythical to most scholars since builders in such ancient times would be considered incapable of building a structure nearly 2.5 kilometers tall. The other extra-canonical source is found in the Third Apocalypse of Baruch; it mentions that the tower reached a height of 463 cubits (694 feet and 6 inches, 212 meters high). This would be taller than any other structure built in the ancient world such as the Pyramid of Cheops in Giza, Egypt and taller than any structure built in human history until the construction of the Eiffel Tower in 1889. While a tower of such a height in the ancient world would have been so incredible as to warrant its reputation and mention in the Bible and other historical texts, it also would be well outside the range of engineering feasability for ancient builders

The height of the tower is largely a matter of speculation, but since the tower symbolically can be considered a precursor to man's desire to build tall structures throughout history, its height is a significant aspect of its mythos. The historic Tower commissioned by Nebuchadnezzar in about 560 BC in the form of an eight level ziggurat is believed by historians to have been about 100 meters (328 feet) in height. The biblical Tower of Babel however would have been built about 2000 years earlier. The narrative in the book of Genesis does not mention how tall the tower was, and thus it has not been much of a subject of debate among fundamentalist Christians. There are however two extra-canonical sources that mention the tower's height. The Book of Jubilees mentions the tower's height as being 5433 cubits and 2 palms (8,150 feet, 2,484 meters high). This would be approximately four times taller than the world's tallest structures of today and in all of human history. Such a claim would be considered as mythical to most scholars since builders in such ancient times would be considered incapable of building a structure nearly 2.5 kilometers tall. The other extra-canonical source is found in the Third Apocalypse of Baruch; it mentions that the tower reached a height of 463 cubits (694 feet and 6 inches, 212 meters high). This would be taller than any other structure built in the ancient world such as the Pyramid of Cheops in Giza, Egypt and taller than any structure built in human history until the construction of the Eiffel Tower in 1889. While a tower of such a height in the ancient world would have been so incredible as to warrant its reputation and mention in the Bible and other historical texts, it also would be well outside the range of engineering feasability for ancient builders. This is the article from Wikipedia...I posted it then realised someone had already beat me to the punch...sorry