A quality score (or Q-score) expresses an error probability. In particular, it serves as a convenient and compact way to communicate very small error probabilities.
Given an assertion, A, the quality score, Q(A), expresses the probability that A is not true, P(~A), according to the relationship:
Q(A) =-10 log10(P(~A))
where P(~A) is the estimated probability of an assertion A being wrong.
The relationship between the quality score and error probability is demonstrated with the following table:
In FASTQ files, quality scores are encoded into a compact form, which uses only 1 byte per quality value. In this encoding, the quality score is represented as the character with an ASCII code equal to its value + 33. The following table demonstrates the relationship between the encoding character, its ASCII code, and the quality score represented.