Limit of Blank, Detection and Quantitation Calculator
Limit of Blank, Detection and Quantitation Calculator
Compute LoB and LoD the way CLSI EP17 defines them, from blank and low-level imprecision — and find out why the limit of quantitation is not a formula at all.
Limit of Blank, Detection and Quantitation
Blank + low-level SD → LoDA high-sensitivity assay reporting in ng/L: 60 blank measurements with a mean of 0.5 and an SD of 0.8, and 60 low-level measurements with a pooled SD of 1.2, at the CLSI default 5% beta error
Formula
LoD = LoB + z1−β × SDlow level
LoQ = the lowest concentration whose observed CV meets a pre-set goal
— a measurement, not a formula — and always ≥ LoD
- 1.645 in the LoB
- z at the 95th centile. It fixes the false-positive rate at 5%: a truly blank sample will read above the LoB about one time in twenty. Choosing a smaller alpha raises the LoB and makes the assay look less sensitive while making a positive call more trustworthy
- z1−β in the LoD
- the false-negative multiplier, and a separate choice from the first. At the CLSI default of β = 5% it is also 1.645, which is why the two numbers look like the same constant used twice; they are not. β = 10% gives 1.282 and β = 1% gives 2.326
- SDlow level
- the pooled standard deviation of samples containing a little analyte, not of the blanks. Imprecision near the bottom of the range is almost always larger than blank imprecision, which is why LoD sits well above LoB and why an LoD derived from blank scatter alone is optimistic
- how many measurements
- EP17 asks for at least 60 blank and at least 60 low-level measurements to establish the limits, and 20 of each for a laboratory verifying a manufacturer’s claim. The low-level 60 come from five independently prepared samples with at least six replicates each, spread over several days, runs and reagent lots. These counts govern how precisely the SDs are known — they do not change the z values, which are set by the alpha and beta you chose
- the small-sample correction
- EP17-A2 does apply one adjustment for how many measurements you made, because an SD estimated from a finite sample is biased low. The multiplier becomes 1.645 ÷ (1 − 1⁄4f) with f the degrees of freedom. At the guideline’s minimum of 60 blanks that factor is 1.0043, taking 1.645 to about 1.652 — a 0.4% change, which is why the plain z is what everyone quotes. The point stands that the replicate count affects the precision of the SD, not the confidence level you asked for
- when the blanks are not Gaussian
- use the non-parametric LoB instead: the 95th percentile of the ranked blank results, at rank 0.5 + 0.95N, interpolating between adjacent ranks. Blank distributions are often skewed or truncated at zero, so this is a real alternative rather than a footnote — and it needs more blanks than the parametric form to pin down a percentile that far into the tail
- LoQ
- the lowest concentration at which the analyte can not only be detected but reported as a number. It is found by measuring imprecision at several low concentrations and taking the lowest one whose CV meets a goal set in advance — 20% is the usual convention, and is where the term functional sensitivity comes from. There is no formula, and any page that gives you one has substituted a different framework
- not the ICH formulas
- pharmaceutical method validation uses LOD = 3.3σ⁄S and LOQ = 10σ⁄S, with σ the response standard deviation and S the calibration slope. Those come from a different guideline with different assumptions and they are not interchangeable with EP17’s. Say which framework you used
Worked example
A high-sensitivity assay reporting in ng/L: 60 blank measurements with a mean of 0.5 and an SD of 0.8, and 60 low-level measurements with a pooled SD of 1.2, at the CLSI default 5% beta error
LoB = 0.5 + 1.645 × 0.8 = 0.5 + 1.316 = 1.82 ng/L — a truly blank sample reads above this about one time in twenty
LoD = 1.816 + 1.645 × 1.2 = 1.816 + 1.974 = 3.79 ng/L
Read that as: a sample containing 3.79 ng/L will read above the LoB at least 95% of the time, so a result above the LoB is unlikely to have come from a blank and a sample at the LoD is unlikely to be missed
Change the beta error to 10% and the multiplier falls to 1.282, giving LoD = 1.816 + 1.538 = 3.35 ng/L. The assay has not changed; you have agreed to miss twice as many samples at the limit
Change it to 1% and the multiplier rises to 2.326, giving 4.61 ng/L. A more cautious claim, and a worse-looking one
What none of this gives you is the LoQ. Suppose you measure a sample at 6 ng/L twenty times and find a CV of 23%, and a sample at 9 ng/L and find 17%. Against a 20% goal the LoQ lies between the two and is nearer 9 than 6 — and no arithmetic on the blank and low-level SDs above could have told you that, because neither of them was measured at 6 or 9 ng/L
If the 60 blanks were skewed rather than Gaussian, the parametric LoB is replaced by the 95th percentile of the ranked blanks, at rank 0.5 + 0.95 × 60 = 57.5 — the average of the 57th and 58th values
The three limits are three different claims
| What it answers | How it is found | What you may do with a result at it | |
|---|---|---|---|
| LoB | What is the highest reading a sample with no analyte is likely to give? | Mean of the blanks + 1.645 SD, or the 95th percentile of the ranked blanks | Nothing. A result at the LoB is indistinguishable from a blank |
| LoD | What is the lowest concentration that will reliably read above the LoB? | LoB + z1−β × the pooled low-level SD | Say the analyte is present. Not report a number |
| LoQ | What is the lowest concentration I may report as a figure? | Measured: the lowest concentration whose CV meets a goal set in advance, commonly 20% | Report the number, and use it for monitoring |
What changes the LoD, and what does not
| Change | Effect on the LoD | Why |
|---|---|---|
| Beta error 5% → 10% | 3.79 → 3.35 ng/L | A smaller multiplier because you have accepted more missed detections |
| Beta error 5% → 1% | 3.79 → 4.61 ng/L | A larger multiplier because you have demanded more certainty |
| Halve the blank SD | 3.79 → 3.13 ng/L | The LoB falls by 1.645 × 0.4; the low-level term is untouched |
| Halve the low-level SD | 3.79 → 2.80 ng/L | The larger of the two levers here, because the low-level SD is the larger SD |
| Run 200 blanks instead of 60 | No change to the multiplier | More measurements make the SD better known; they do not change the confidence level you chose. EP17-A2’s small-sample correction moves the multiplier by 0.4% at 60 and less above that |
| Use water instead of analyte-free matrix | Usually falls — misleadingly | A blank without the matrix understates the noise the assay will actually meet, and produces a detection limit the assay cannot deliver on patient samples |
Three limits, two of them formulas and one of them a measurement
Every assay has a floor, and describing it takes three numbers rather than one. The limit of blank is the highest result a sample containing no analyte is likely to produce: the mean of a set of blank measurements plus 1.645 of their standard deviations, which fixes the false-positive rate at 5%. The limit of detection is the lowest concentration that will reliably read above that: the LoB plus a further multiple of the imprecision of low-level samples, where the multiplier sets the false-negative rate. The limit of quantitation is the lowest concentration you may actually report as a figure — and it is not derived from either of the other two.
The two multipliers look like the same constant used twice and they are two separate decisions. The 1.645 in the LoB is z at the 95th centile and controls how often a blank sample is wrongly called positive. The multiplier in the LoD is z at 1 − β and controls how often a sample at the detection limit is wrongly called blank. CLSI’s default sets both error rates at 5%, so both multipliers come out at 1.645, which is why so many summaries write the formulas as though one constant were being reused. Move β to 10% and the second becomes 1.282; move it to 1% and it becomes 2.326. On the worked example those choices change the detection limit from 3.79 to 3.35 or to 4.61 ng/L, with no change whatever in the assay. Say which error rates you used.
What the replicate counts do is a separate question, and it is worth being precise because it is widely muddled. EP17 asks for at least 60 blank and at least 60 low-level measurements to establish the limits, and 20 of each for a laboratory verifying a manufacturer’s claim, with the low-level 60 built from five independently prepared samples of at least six replicates each spread across days, runs and reagent lots. Those counts determine how precisely the two standard deviations are known. They do not change the confidence level, because that was set by the alpha and beta you chose. There is one genuine exception, and it is small: EP17-A2 divides the multiplier by (1 − 1⁄4f), with f the degrees of freedom, to correct for the downward bias of an SD estimated from a finite sample. At 60 blanks that factor is 1.0043 and turns 1.645 into 1.652. Worth knowing about; not worth arguing over.
The parametric formulas assume the blank results are roughly normally distributed, and blank distributions frequently are not — they are skewed, or piled against a floor at zero because the instrument will not report a negative number. EP17 provides for this: take the 95th percentile of the ranked blank results instead, at rank 0.5 + 0.95N, interpolating between the adjacent values. With 60 blanks that is rank 57.5, the average of the 57th and 58th. A percentile that far into the tail is poorly estimated from few observations, so a non-parametric LoB wants more blanks than a parametric one, not fewer.
Which leaves the limit of quantitation, and the honest statement about it is that there is no formula. The LoQ is the lowest concentration at which the analyte can not only be detected but measured with a precision you have specified in advance — conventionally a CV of 20%, which is where the term functional sensitivity comes from. It is found by measuring imprecision at a series of low concentrations and taking the lowest one that meets the goal. Nothing about the blank SD or the low-level SD can produce it, because neither was measured at the concentration in question. The LoQ is always at or above the LoD, often well above it, and the gap between them is real territory: a result there means the analyte is genuinely present and the number attached to it is too imprecise to act on or to compare with a previous result. One further caution. Pharmaceutical method validation uses a different framework entirely — LOD = 3.3σ⁄S and LOQ = 10σ⁄S, from the calibration response and slope — and those formulas will not give you EP17’s answers. Both are legitimate; mixing them is not.
Frequently asked questions
How do you calculate the limit of blank and limit of detection?
LoB is the mean of the blank measurements plus 1.645 times their standard deviation, which sets a 5% false-positive rate. LoD is the LoB plus z at 1 − β times the pooled standard deviation of low-level samples, which is 1.645 again at CLSI’s default 5% false-negative rate. With a blank mean of 0.5, a blank SD of 0.8 and a low-level SD of 1.2, LoB is 1.82 and LoD is 3.79.
What is the formula for the limit of quantitation?
There isn’t one, and this is the most important thing on the page. The LoQ is the lowest concentration whose observed imprecision meets a goal set in advance — commonly a CV of 20%, which is what functional sensitivity means. You find it by measuring the CV at several low concentrations, not by arithmetic on the blank and low-level standard deviations. It is always at or above the LoD.
How many blank and low-level measurements does CLSI EP17 require?
At least 60 of each to establish the limits, and 20 of each for a laboratory verifying a manufacturer’s claim. The low-level measurements should come from five independently prepared samples at concentrations one to five times the LoB, with at least six replicates each, spread across several days, runs and reagent lots.
Does the multiplier change if I run more replicates?
Essentially no. The 1.645 is set by the error rate you chose, not by the sample size, so more replicates make the standard deviation better known rather than the limit smaller. EP17-A2 does apply a small-sample correction, dividing the multiplier by (1 − 1/4f) with f the degrees of freedom, which at 60 blanks turns 1.645 into 1.652 — a 0.4% change.
What if the blank measurements are not normally distributed?
Use the non-parametric LoB: the 95th percentile of the ranked blank results, at rank 0.5 + 0.95N, interpolating between adjacent values. Blank distributions are often skewed or truncated at zero by an instrument that will not report negative numbers, so this is a routine alternative rather than an exotic one. It needs more blanks than the parametric form, because a percentile that far into the tail is poorly estimated from few results.
Can I report a result that falls between the LoD and the LoQ?
You can say the analyte was detected; you should not report a figure. Between those two limits the analyte is genuinely present and the number attached to it does not meet your own precision specification, so it cannot support a clinical decision and cannot be compared with a previous result. The usual convention is to report such results as less than the LoQ, with the LoQ stated.
Related calculators
References
- CLSI EP17-A2. Evaluation of Detection Capability for Clinical Laboratory Measurement Procedures; Approved Guideline. 2nd ed. Clinical and Laboratory Standards Institute; 2012 (reaffirmed 2017).
- Armbruster DA, Pry T. Limit of blank, limit of detection and limit of quantitation. Clin Biochem Rev. 2008;29(Suppl 1):S49–S52.
- Currie LA. Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995). Pure Appl Chem. 1995;67(10):1699–1723.
- ICH Q2(R2). Validation of Analytical Procedures. International Council for Harmonisation; 2023 — the source of the different LOD = 3.3σ/S and LOQ = 10σ/S conventions.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.