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Can someone calculate, from books description or from movies, the height of Barad-dûr?

I've found this on FB but it sounds too small to me!!

Scale drawing showing black-and-white silhouettes of famous buildings against a scale graded in hundreds of metres.  From the left, the Great Pyramid is about 150m, the Eiffel Tower is over 300m, the Empire State Building is over 400m including its mast, the Petronas Towers are 400m plus short antennae, Taipei 101 is nearly 500m, The CN Tower is over 500m, Burj Dubai is 800m and Barad-dûr is over 1400m tall.

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    Too small? It is stupendous! To me it seems too tall, considering there were no elevators!
    – user13809
    Apr 14 '13 at 0:42
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    Notice the building doesn't actually start until the ~400m mark. Making the building approximately 1000m high, a mere 200m higher than the tallest "real" building.
    – E.T.
    Apr 14 '13 at 10:39
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    The tallest real building is tall as hell though.
    – Misha R
    Apr 1 '15 at 5:42
  • In the real world, the tallest building constructed of brick without steel beams is only 16 stories high. Presumably a stone tower could be taller, but... May 4 '21 at 3:17
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Tolkien intentionally left details of the tower's construction and appearance vague. It was described as behind hidden by a cloud of shadow and darkness (probably both literal and metaphorical).

...rising black, blacker and darker than the vast shades amid which it stood, the cruel pinnacles and iron crown of the topmost tower of Barad-dûr...

The Lord of the Rings 6 III: Mount Doom

According to the Lord of the Rings wiki, the miniature model used in the movie (which Weta actually called "bigatures" since they would still dwarf a person) was the equivalent of around 1,500 meters (5,000 feet) tall. The movie also depicts it as visible from the Black Gate, which is 100 miles away (according to the books' geography), so that certainly sounds reasonable.

One of the comments on this thread on Planet Tolkien uses a number of passages from the books about Orthanc and Minas Tirith to attempt to estimate the height of the tower and comes up with somewhere on the order of 3,000 feet tall.

It looks like the image you found uses the Weta/bigature/to-scale measurement. How is that too small? It's 1.5 kilometers (almost a mile)! It's twice as big as the largest real building ever made, which is itself already absurdly tall!

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