A measure of how easy it is to fully harden a steel is known as its hardenability. The higher the hardenability, the easier it is to harden and the slower the quenching rate can be. It is the quantity and type of alloy in the steel that determines its hardenability.
Steels with high hardenability can be fully hardened easily, by quenching in air for example. Those with low hardenability are difficult to fully harden and need to be quenched in water.
Another way to consider hardenability is in terms of how large a diameter of bar can be fully hardened to its centre by a given quenching method. For example, after oil quenching, a low hardenability steel might only fully harden in a bar 2cm thick whereas a high hardenability steel might fully harden in a bar 15 cm thick.
A steel’s hardenability is determined by its alloy content. The maximum hardness of a steel after it has been fully hardened is determined by its carbon content, not its hardenability.