These words refer to quantities or sizes that are great, infinite or difficult to determine. Countless refers to large amounts that are difficult or impossible to total either because of their vastness or because their full extent is not known or unknowable: countless grains of sand scattered by the wind. Though the visible stars in the sky are often hyperbolically referred to as countless , they have in fact been counted, as well as those studied by other means. In the strictest sense, only those that may exist beyond any observation are countless , though these may be few or great or even infinite in number. Similarly, countless may refer to large quantities that cannot now be totalled: the countless numbers who died of malaria before the discovery of quinine. While countless may sometimes refer to instances in time and innumerable may refer to quantities in space, the latter is particularly used for occurrences that cannot be totalled because of frequency or lack of record: innumerable instances in the past when a new idea was found dangerous to the established order. The word is frequently used merely as a hyperbole for may: innumerable occasions on which he had stayed out all night carousing.

Immeasurable refers more strictly to spatial size or to dimensions that are either infinite or completely impossible to determine. Thus, unlike countless and innumerable , the word is less likely to be used hyperbolically, whether to refer to greatness or difficulty of reckoning: distances that in an infinite universe would be literally immeasurable ; immeasurable quantities of natural resources that were lost forever through misuse. Incalculable most strictly resembles the first pair of words in referring to large amounts difficult to total. The word may also be used like immeasurable for large volumes, but in this case the size may be hard to determine because of its uncertain dimensions: a deep trough on the sea floor, one of incalculable size. More commonly, however, the word refers particularly to the effects something has, when these are difficult or impossible to determine or can never be known: the incalculable effects of Luther’s break with Rome, effects that still have not run their course; the incalculable benefits that ripple outwards from even the most trivial act of kindness; aware that he was taking an incalculable risk.