Time-to-flood is a key parameter during a flooding emergency. Especially in complex geometries, it is important to know the time needed to fill the first flooded room, i.e., the damaged one. Here, a fast solution for the assessment of the time-to-flood of one or two parallelepiped rooms is proposed. The progressive flooding of the rooms is first simulated employing a linearised simulation technique that defines a database of damage cases covering a wide range of geometries. Explicit equations are then defined based on the main non-dimensional parameters governing the phenomenon. The work highlights the relationship between the geometry of a room, the damage opening, the connection opening, and the time to fill the first damaged room. The application of the equations is very fast and provides an instantaneous estimation of the time-to-flood. This makes them particularly suitable for direct application on board or when creating large datasets of flooding simulations.