It's the question every cruise passenger wonders about, and one that was articulated in the opening credits of ITV's recent fly-on-the-wall docudrama, The Cruise.
Arriving at the quayside to start her holiday aboard Royal Princess, one woman gazed up at her home for the next week, and proclaimed: "Beautiful! Makes you wonder how they keep afloat."
The vessel might have the Duchess of Cambridge as a godmother - she was heavily pregnant with Prince George when she cut the ribbon in 2013 - but to most eyes she's no beauty.
At 330 metres long, she is longer than the Manchester United, Arsenal and Liverpool football pitches laid end-to-end. The vessel's 17 passenger decks, with their serried ranks of balconies, reach a height of 66 metres - taller than Nelson's Column with a couple of Routemaster buses piled on top.
At Promenade Deck level, she is 38.4 metres wide. Higher up, the Lido Deck overhangs the side of the ship and a Sea Walk projects outwards for a further 26 feet.
Below the waterline there's only 8.5 metres to the keel. That's just over 10 per cent of the ship's bulk.
So how does it stay afloat? How does it resist being blown over in a gale, or toppled by rough seas? What stops it from capsizing if the ship is forced to make a sharp turn?
Let's remember that it is also burdened with the weight of 3,500 passengers and all their luggage. Not to mention the food required to keep them sated, the thousands of tables and chairs in restaurants, bars and theatres, beds, bathrooms, the swimming pools, the marble-clad atrium, the lifts, and everything else required to service a floating hotel.
But, despite all of those things and more, the vessel is full of air. Imagine a bowling ball and a beach ball side by side. Drop them in the sea and the beach ball will float, high in the water.
Let's dispel another myth before starting to look at the physics.
Although the size of a ship is calculated on its tonnage, this is a measure of volume rather than weight. It is defined by the ship's enclosed internal space.
A ship's weight is measured by the amount of water it displaces. Royal Princess, for example, is 142,714 gross tonnes, and while sister ship Majestic Princess is almost the same size it measures 143,000 gross tons for the simple reason that there is a glass roof covering one of its swimming pools.
Despite the seemingly unfeasible height relative to the volume below the waterline, its centre of gravity is kept low because the heaviest equipment - its engines - are below decks, along with the tanks containing fuel, waste, and drinking water. There are also ballast tanks, containing water that can be pumped from one end of the ship to the other, and from port to starboard, to maintain stability.
Now, the physics. A cruise ship displaces an amount of water equivalent to its own mass. The pressure of the sea pushes up against the vessel's hull to counter the downward force of the ship's mass. Unlike air, water cannot be compressed, so the combined forces create buoyancy.
It's basically the principle discovered when Archimedes took a bath 2,300 years ago and ran naked through the streets of Syracuse in celebration.
The water a cruise ship displaces becomes the waves and wash it creates as it moves along. A rounded U-shaped hull is preferable for creating buoyancy; some ships are flat-bottomed and while they still float, they are likely to move uncomfortably in heavy seas.
Staying afloat is the abiding principle of a cruise ship, but the hull must also be designed to resist obstacles such as concrete piers, rocks, sandbars, and even icebergs.
Inside, a series of separate compartments with automatic watertight doors prevent the hull filling completely with water. On the Titanic, those compartments did not reach high enough and water overflowed from one to another.
On the ill-fated Costa Concordia, the captain's action in sailing too close to rocks breached several compartments at once and his subsequent actions in trying to turn the ship caused the ship to tilt, or list, with fatal consequences.
International regulations have now changed to ensure that no captain could single-handedly take the wilful decisions that cost 33 lives on Concordia.
As an aside, the same watertight compartments also prevent the spread of fire - a maritime catastrophe feared even more than sinking.
It's one of life's great ironies that the popularity of cruising today is based on the glamorous image projected in a film about the sinking of an ocean liner 105 years ago. The 25 million passengers who cruise each year now do so safe in the knowledge that a repeat of the Titanic disaster is infinitely less likely than the chances of them ever owning a private yacht.