Phred Quality Scores: What Q20, Q30, Q40 Mean

A Phred quality score is not a measurement of how good a base is. It is the base caller’s prediction of the probability that it got that base wrong, expressed on a negative log scale. That distinction drives almost every mistake people make with Q values: treating Q30 as a guarantee, averaging Q scores arithmetically, comparing Q distributions across platforms, or reading a modern binned Q40 as if it were a finely resolved estimate. This guide covers what the number actually asserts, how it is produced, and where it stops being trustworthy.

The definition, and the only table you need

Ewing and Green defined the quality value in the phred base caller as

Q = −10 × log₁₀(P), where P is the estimated probability that the base call is incorrect.

Inverted, P = 10^−Q/10. Because the scale is logarithmic in base 10 with a factor of 10, every 10-point rise in Q is a tenfold drop in predicted error rate. That is the whole scheme.

Q10 — P = 0.1, 1 error in 10, 90% inferred accuracy
Q20 — P = 0.01, 1 error in 100, 99% inferred accuracy
Q30 — P = 0.001, 1 error in 1,000, 99.9% inferred accuracy
Q40 — P = 0.0001, 1 error in 10,000, 99.99% inferred accuracy
Q50 — P = 0.00001, 1 error in 100,000

Illumina publishes the Q10/Q20/Q30 rows of that table directly, and the Q40 and Q50 rows follow from the same formula. The word inferred in “inferred base call accuracy” is doing real work: it is the accuracy implied by the model, not an accuracy anyone measured on your sample.

What Q30 does not mean

Vendor material often frames Q30 as the point where reads are essentially error-free. Per base, Q30 is a 1-in-1,000 error probability. Per read, that compounds. On a 150 bp read where every base is called at exactly Q30:

Expected number of miscalled bases per read = 150 × 0.001 = 0.15
Probability that the read contains at least one error = 1 − (0.999)¹⁵⁰ = about 13.9%

So roughly one read in seven carries a miscall even in a run that looks clean by the Q30 headline. At a uniform Q40 the same 150 bp read has about a 1.5% chance of containing an error. This is why single-read evidence for a variant is worthless and why coverage depth, not Q score alone, is what buys confidence in a call. It is also why unique molecular identifiers and duplex approaches exist for low-frequency variant detection: they attack the per-molecule error floor that Q scores merely describe.

The averaging trap

Q values are logarithms. You cannot take their arithmetic mean and get a meaningful answer. The correct procedure is to convert each Q to its error probability, average the probabilities, then convert back:

Q_mean = −10 log₁₀( mean( 10^−Q_i/10 ) )

Oxford Nanopore’s Dorado basecaller documents exactly this sequence for its per-read mean Q: convert the Q-scores into error probabilities, calculate the mean of the error probabilities, then convert the mean error probability back into a mean Q-score. Dorado also trims the leading 60 bases before doing so, to account for higher than normal noise at the start of a read.

The gap between the two methods is not cosmetic. Take a read that is half Q40 bases and half Q10 bases. The arithmetic mean of the Q values is 25, which reads as a respectable 1-in-316 error rate. The probability-weighted mean is Q13 — a 1-in-20 error rate, because the handful of terrible bases dominate the expected error count and the excellent bases cannot rescue them. Any tool or spreadsheet that reports a “mean quality” without telling you which method it used should be treated as suspect, and any filter threshold built on an arithmetic mean is looser than it looks.

Where the number comes from

Phred scores are not derived from first principles. They come from a calibration table built by observing real errors.

In the original phred program, Ewing and Green estimated a probability of error for each base call as a function of certain parameters computed from the trace data, then validated that those probabilities were valid — that is, that they corresponded to actual error rates — across several different chemistries and electrophoretic conditions. The companion paper reported that phred achieved a lower error rate than the contemporaneous ABI base caller, averaging 40–50% fewer errors in the data sets examined. That empirical grounding is the reason the scale was adopted so widely; see our guide to Sanger sequencing and reading a trace for how those trace parameters arise in the first place.

Modern short-read instruments do the same thing with different predictors. Illumina states that each base in a read is assigned a quality score by a phred-like algorithm, similar to that originally developed for Sanger sequencing experiments, using the same Q = −10 log₁₀(e) formula. The predictor set and the calibration table are instrument-, chemistry- and software-version-specific and are not published in full, which has a practical consequence: a Q30 from one platform and a Q30 from another are two different models’ opinions, not a common physical unit. Comparing raw Q distributions across platforms tells you about their calibration habits at least as much as about their data.

Calibration drifts, and that is why recalibration exists

Instrument-reported quality scores are systematically imperfect. DePristo and colleagues, describing the GATK framework, noted that per-base quality scores are quite inaccurate and co-vary with features like sequencing technology, machine cycle and sequence context, and that the inaccuracy and covariation patterns differ strikingly between sequencing technologies, which if uncorrected can propagate into downstream analyses. Base Quality Score Recalibration re-derives empirical quality from observed mismatch rates against a set of known variant sites, modelled across covariates including machine cycle and dinucleotide context. In their HiSeq data set, recalibration eliminated approximately 300,000 SNP calls, over 20% of the raw novel calls — a useful sense of how much a miscalibrated Q can distort a variant list.

The operational point: if your pipeline calls variants, the Q values in your BAM after recalibration are not the Q values the instrument wrote, and QC run on the raw FASTQ is answering a different question from QC run on the analysis-ready BAM.

Reading Q values out of a file without corrupting them

Q scores are stored as single ASCII characters, which means an offset convention has to be agreed. Cock and colleagues catalogued the incompatible variants in their FASTQ format paper:

Sanger / fastq-sanger (Phred+33) — ASCII 33 to 126, Q range 0 to 93. This is the modern default and what the SAM specification requires.
Solexa / fastq-solexa (Solexa+64) — ASCII 59 to 126, score range −5 to 62. Note the negative floor: these are not Phred scores at all.
Illumina 1.3+ / fastq-illumina (Phred+64) — ASCII 64 to 126, Q range 0 to 62.

In Phred+33, Q0 is ! (ASCII 33), Q30 is ? (ASCII 63) and Q40 is I (ASCII 73). The SAM specification defines QUAL as “ASCII of base QUALity plus 33 (same as the quality string in the Sanger FASTQ format)”, with a base quality being the phred-scaled base error probability equal to −10 log₁₀ Pr{base is wrong}, and permits * when quality is not stored.

The failure mode to watch for: Cock and colleagues warn that the incompatible FASTQ variants cannot be reliably distinguished from the file contents alone without knowing the source. Misreading a Phred+64 file as Phred+33 inflates every score by exactly 31 — the character h is a legitimate Q40 under Phred+64 and a nonsensical Q71 under Phred+33. The reverse mistake produces negative scores. If a legacy data set suddenly shows implausibly high or negative qualities, suspect the offset before you suspect the run. The same paper flags a parsing hazard worth knowing: the @ marker character (ASCII 64) may occur anywhere in the quality string, including at the start, so a parser must not treat a line beginning with @ as the start of the next record.

Solexa scores use a log-odds scale, Q_solexa = −10 log₁₀(P / (1 − P)), and convert to Phred as Q_phred = 10 log₁₀(10^Q_solexa/10 + 1). The conversion is lossy at the bottom of the range: Solexa 9 and Solexa 10 both round to Phred 10. Getting encodings right matters beyond your own analysis — archives validate what you deposit, so check the expected encoding before submitting sequence data to NCBI SRA.

Binned Q scores: the resolution you no longer have

On current Illumina instruments the Q value in your FASTQ is usually not a per-base estimate at all. It is a bin label. Illumina’s BaseSpace documentation confirms that Q-scores are automatically binned on supported systems and that only the subset of Q-scores applied by the bins is displayed.

Illumina’s published RTA4 bin ranges for the NovaSeq X and X Plus make the coarseness concrete. Each reported value is described as an average for the range of called scores:

Control Software v1.3 — bin 2 (NoCall, 0–2), bin 9 (3–17), bin 24 (18–29), bin 40 (30+)
Control Software v1.2 / v1.2.2 — bin 2 (NoCall, 0–2), bin 12 (3–17), bin 24 (18–29), bin 40 (30+)

Three things follow. First, a base labelled Q40 in such a file may have an underlying estimate anywhere from 30 upward; the label is a bin, not a measurement. Second, a “percent bases ≥ Q30” metric computed on binned data is close to a count of how many bases landed in the top bin, so it is far less informative than the same metric on unbinned output. Third, the bin values themselves changed between control software versions on the same instrument, so a Q-score histogram is not comparable across a software upgrade. Always record the instrument and software version alongside QC figures. Exact bins for other instruments and RTA versions differ — check the vendor documentation for the specific platform and software release rather than assuming these values transfer.

Binning exists to cut file size and bandwidth. The vendor position is that it does so without affecting accuracy or performance for standard applications, but for anything that leans on fine-grained quality gradients — low-allele-fraction somatic calling, error-model fitting — you should confirm whether unbinned output is available for your instrument rather than assume the label resolution you see.

Not every Phred-scaled number is a base quality

The Phred transform is used all over genomics for quantities that are not base calls, and conflating them is a common source of confusion when reading a BAM or VCF.

Base quality (QUAL string in FASTQ/SAM) — Pr{this base is wrong}.
MAPQ — the SAM spec defines it as “MAPping Quality. It equals −10 log₁₀ Pr{mapping position is wrong}, rounded to the nearest integer”, with 255 meaning the mapping quality is not available. A MAPQ of 60 says nothing about base accuracy; it says the aligner is confident about where the read goes.
VCF QUAL and genotype quality — Phred-scaled confidence in a variant or genotype call, aggregated over many reads. These routinely reach values far above any single base quality precisely because they pool evidence.

A read can have flawless base qualities and a MAPQ of 0 because it maps equally well to two repeats. A variant can have a high QUAL built entirely from mediocre bases at high depth. Read the field, not the scale.

Practical use in QC

Q scores earn their keep as a relative and positional signal more than as an absolute threshold.

Look at quality as a function of cycle. A decline toward the 3′ end is expected on sequencing-by-synthesis chemistry; an abrupt collapse, or a dip in the middle, points at a run problem rather than normal decay.
Compare against the run’s own control. A spike-in such as PhiX control gives a known template against which the empirical error rate can be measured directly, which is the closest thing to a ground-truth check on whether the reported Q values are honest for that run.
Do not hard-trim on Q by reflex. Aggressive quality trimming shortens reads and can bias downstream quantification; many modern aligners and variant callers model base quality natively and prefer to see the data. Trimming policy is application-specific — the tradeoffs differ substantially between variant calling and expression work, as covered in our RNA-seq design and analysis guide.
Treat pass/fail thresholds as local. There is no universal minimum Q. Acceptable values depend on platform, chemistry, application, target depth and the vendor’s own run specification. Where a threshold is quoted in a protocol, trace it to the instrument specification or the assay validation that produced it, and record which one you used.

Frequently asked questions

What is a good Phred score?

There is no platform-independent answer, and any single number quoted without context is vendor- or application-dependent. What is fixed is the arithmetic: Q20 is a 1-in-100 predicted error rate, Q30 is 1-in-1,000, Q40 is 1-in-10,000. Which of those is adequate depends on your application and your depth. For high-depth germline variant calling, per-base quality matters less than coverage and mapping quality; for low-frequency variant detection, no per-base Q is sufficient on its own and molecular tagging is the usual answer. Judge a run against the instrument’s published specification and against your own historical runs on the same assay.

Why does my FASTQ have quality characters that decode to impossible scores?

Almost always an encoding-offset mismatch. Phred+64 data read as Phred+33 adds 31 to every score, producing values above the plausible range; Phred+33 data read as Phred+64 produces negatives. Because the variants cannot be reliably distinguished from file contents alone, tell your tools the encoding explicitly when you know the provenance, and be sceptical of automatic detection on short or unusual files.

Can I average Phred scores to get a read quality?

Not arithmetically. Convert each Q to an error probability, average the probabilities, then convert back. A read that is half Q40 and half Q10 has an arithmetic mean of Q25 but a true mean quality of about Q13. The low-quality bases dominate the expected error count, which is precisely what a mean quality is supposed to capture.

Why does my NovaSeq FASTQ contain only a handful of distinct Q values?

Q-score binning. Illumina’s RTA software collapses the estimate into a small number of bins to reduce storage and bandwidth; on the NovaSeq X and X Plus with Control Software v1.3, the reported values are 2, 9, 24 and 40, each standing in for a range of underlying scores. This is expected behaviour, not corruption, but it does mean the fine structure of the quality distribution is gone.

Is a Phred score a measurement or a prediction?

A prediction. It is the output of a calibration model that maps signal features to an expected error rate, and it is only as good as that calibration. Ewing and Green validated that phred’s probabilities corresponded to actual error rates on the data they examined; on modern platforms, reported qualities are known to co-vary with cycle and sequence context, which is the entire motivation for base quality score recalibration in variant-calling pipelines.

Is Q30 the same thing on every sequencer?

Only as arithmetic. Q30 always denotes a predicted 1-in-1,000 error rate, but each platform derives that prediction from its own proprietary calibration against its own error modes. Two platforms reporting the same Q distribution can have quite different real-world error profiles, and their errors are of different kinds. Compare empirical error rates against a known control rather than comparing reported Q histograms.

Why is my per-base quality high but my variant calls still wrong?

Base quality is one of several independent things that can go wrong. The read may be misplaced, which is a mapping-quality problem, not a base-quality one. The error may be a systematic artefact that the base caller is confident about, such as a context-specific miscall that recalibration is designed to expose. Or the quality scores themselves may be miscalibrated for that run. High QUAL characters are a necessary but nowhere near sufficient condition for a correct call.