How a floating dock lifts a battleship

How is the lifting capacity of a floating dry dock calculated?

Designers combine dock and ship weight, then provide enough buoyant volume and de-ballasting capacity for the whole system to displace more water than it weighs.

The calculation starts with the structural weight required for a dock strong enough to support the intended ship. The vessel's displacement is then added to establish the combined load that must be lifted. By emptying ballast spaces and replacing water with air, the dock lowers its average density and increases buoyancy. It rises when the combined structure displaces more water weight than its own total weight. This is a conceptual calculation of the relationship between displacement, density, and ballast; detailed engineering calculations are not supplied.