How many people were aboard the Titanic?

How to get close to this number

Reason from the ship rather than the story. A transatlantic liner of that era carried a crew of several hundred and passengers in the low thousands. Crew plus passengers puts the figure just over two thousand, and the explanation adds that the ship was well below its full capacity of around three thousand three hundred.

The lifeboat arithmetic is the part that matters and it is the reason the disaster is studied. Capacity for barely half those aboard was legal at the time because regulations scaled with the ship's tonnage rather than with how many people it carried — a rule written when ships were smaller and never updated as they grew.

That is the general lesson worth keeping: a regulation indexed to the wrong variable fails silently as the world changes around it. The ship complied fully with the law and the law was wrong, which is a failure mode that recurs across safety engineering and is much harder to detect than outright violation.