Iceberg freeboard ($F=H-{\rho }_w^{-1}{\int }_0^H{\rho }_i(z)dz$)

For a vertical-sided floating iceberg of height $H$, Archimedes' principle equates displaced water mass to ice mass. Its draft is ${\rho }_w^{-1}{\int }_0^H{\rho }_i(z)dz$ and its freeboard is the remaining height above water. A depth-dependent mass density must be integrated; using the densest layer throughout overestimates the draft.