Usefulness, n.
The quality or state of being useful; utility; serviceableness; advantage. Addison.
Syn. -- Utility; value; profit. See Utility.
Shades of meaning
Fernald has no entry of its own for usefulness; he lists it under profit, utility.
Where he writes about it:
Utility (L. utilis, useful) signifies primarily the quality of being useful, but is somewhat more abstract and philosophical than usefulness or use, and is often employed to denote adaptation to produce a valuable result, while usefulness denotes the actual production of such result. — from utility
We say of an invention, its utility is questionable, or, on the other hand, its usefulness has been proved by ample trial, or I have found it of use; still, utility and usefulness are frequently interchanged. — from utility