FASTQ Base Quality Calculator

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Background
Base quality scores represent the sequencer's confidence that a nucleotide was accurately called (sometimes called Phred quality score). Inside FASTQ files, these numerical scores are stored as characters. Here is an example FASTQ record, with the base quality highlighted:
@read1
ACGTACGTACGT
+
!!IIIIII87II
 Read name
 DNA sequence
 Ignored line
 Base quality
Calculator
 
Quality
ASCII
Prob.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~
1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9

A quality score of 20 is represented as the character 5 in FASTQ files, and corresponds to a base calling error probability of 1.0e-2, or 1 in 100.