A function is Turing computable if the function's value can be computed with a Turing machine.

More specifically, let be a set of words in a given alphabet and let be a function which maps elements of to words on the same alphabet. We say that is Turing computable if there exists a Turing machine such that

• If one starts the Turing machine with a word as the initial content of the tape, the computation will halt.
• When the computation halts, the tape will read .

Because of the fact that all types of Turing machines (deterministic, non-deterministic, single head, multiple head, etc.) all have the same computational power, it does not matter which type of Turing machine one uses in the definition.

It is not hard to find examples of Turing computable functions -- because Turing machines provide an idealized model for the operation of the digital computer, any function which can be evaluated by a computer provides an example.