Scholarly estimate from Tolkien's descriptions

Photo from Wikimedia Commons
Barad-dur (Sauron's Dark Tower)
Middle-earth's tallest tower, forged with the power of the One Ring/Mythical & Fictional
Barad-dur, the Dark Tower of Mordor in J.R.R. Tolkien's Lord of the Rings, was Sauron's fortress and the second tallest structure in Middle-earth's history after Thangorodrim. Based on descriptions in the text, scholarly estimates place its height at roughly 460 meters, with foundations laid using the power of the One Ring that could not be destroyed while the Ring endured. The tower housed the great Eye of Sauron at its peak and was surrounded by the desolation of the Plateau of Gorgoroth. It took Sauron 600 years to build and about three seconds to fall once the Ring was destroyed, which is the most dramatic demolition in fictional history.
Measurements
Approximately 600 years
Approximate from text descriptions
The lidless eye at the summit
Once in the Second Age, once in the Third