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I've had this question for a while now and it's: How big is Ancalagon exactly? I mean, I've looked over thousands of explanations but it keeps on changing. So I'm asking now, how big exactly is this dragon?

I don't know if this is mentioned in The Silmarillion but I just wanted to see if there is an exact calculation.

We don't know much! The Silmarillion says:

Before the rising of the sun Eärendil slew Ancalagon the Black, the mightiest of the dragon-host, and cast him from the sky; and he fell upon the towers of Thangorodrim, and they were broken in his ruin.

So all we can do is look at what we know of Thangorodrim. We know that Morgoth came to the ruins of Angband and

There he delved anew his vast vaults and dungeons, and above their gates he reared the threefold peaks of Thangorodrim, and a great reek of dark smoke was ever wreathed about them.

And Feanor, before he dies,

... looking out from the slopes of Ered Wethrin with his last sight he beheld far off the peaks of Thangorodrim, mightiest of the towers of Middle-earth,

"Threefold peaks" makes them sound like mountains, but in another places, Tolkien writes:

and above its doors he reared the reeking towers of Thangorodrim;

"Towers" are not quite so...vast... sounding. Nor does the fact that when

the Elves smote upon the gates of Angband, and the challenge of their trumpets shook the towers of Thangorodrim;

They shook, which does not sound like mountains. (But perhaps this is poetic rather than descriptive?)

Yet, he also says that Morgoth

... piled the thunderous towers of Thangorodrim, that were made of the ash and slag of his subterranean furnaces, and the vast refuse of his tunnellings. They were black and desolate and exceedingly lofty; and smoke issued from their tops, dark and foul upon the northern sky.

But at another time they were volcanoes:

Then suddenly Morgoth sent forth great rivers of flame that ran down swifter than Balrogs from Thangorodrim, and poured over all the plain; and the Mountains of Iron belched forth fires of many poisonous hues...

...Below them suddenly thunder rolled, lightnings leaped upward, and the mountains quaked. Fire and smoke belched forth from Thangorodrim, and flaming bolts were hurled far abroad, falling ruinous upon the lands;

How tall were they? Well, we know that

coming to the skirts of Taur-nu-Fuin he looked out across the waste of Anfauglith and saw afar the peaks of Thangorodrim.

Finally, we know that the meaning of "Thangorodrim" is "Mountains of tyranny".

So, whatever Thangorodrim's peaks were, they were BIG. It seems hard to say more than than -- the three towers may have been Empire State Building sized or they may have been a lot bigger.

What does this tell us about Ancalagon the Black? Well, at the very least it must have been large compared to a modern airplane -- you can't knock down even one Empire State Building sized tower with an airplane unless it is hollow and subsequently gutted by fire. For Ancalagon the destroy all three just by falling on them, it must be several hundred feet long at the least.

And if Thangorodrim's three peaks are volcanoes, Ancalagon must have been vast beyond comprehension.

At the end, I remember that Earendil, in a boat that was probably not more than 100' long, killed Ancalagon and I conclude that maybe he could best a 200' dragon. If Ancalagon is a mile long, all he could do is land on it and engage in trench warfare against Ancalagon's skin parasites...