Coefficient of Variation Calculator
Coefficient of Variation Calculator
Turn an SD and a mean into a CV%, and compare it with the target you are working to. An SD on its own is meaningless — the CV is what makes imprecision comparable between analytes and between levels.
Coefficient of Variation
SD, mean → CV%A month of QC on a glucose method: mean 5.20 mmol/L, SD 0.13 mmol/L, target 5.0%
Formula
- SD
- the standard deviation of a set of repeated measurements, in the analyte’s own units. It carries those units, which is precisely why it cannot be compared between analytes or even between two levels of the same one
- mean
- the mean of the same measurements. The SD must always be quoted with it: an SD of 0.13 is superb at a mean of 5.2 and hopeless at a mean of 0.4
- CV%
- imprecision expressed as a percentage of the mean, which cancels the units and makes the figure comparable across analytes, levels, instruments and laboratories
- how many results
- at least 20 measurements before the SD is stable, and in practice a month of routine QC. A CV from five results is a guess; CLSI EP15 sets out the formal verification protocol
- which level
- always quote the concentration. Imprecision is nearly always worse at low concentrations, so a CV from a high QC level says little about performance at a decision limit near the bottom of the range
Worked example
A month of QC on a glucose method: mean 5.20 mmol/L, SD 0.13 mmol/L, target 5.0%
0.13 ÷ 5.20 = 0.025
0.025 × 100 = 2.5%
That is within the 5.0% target entered, so the method meets its specification at this level
The same SD of 0.13 at a low QC level with a mean of 2.60 mmol/L would be a CV of 5.0% — identical scatter, twice the relative imprecision, and now on the target rather than comfortably inside it
Which is the whole point: 0.13 is not a good SD or a bad one until you say what it is 0.13 of
The same SD at three concentrations
| QC level | Mean (mmol/L) | SD (mmol/L) | CV% |
|---|---|---|---|
| Low | 2.60 | 0.13 | 5.0% |
| Normal | 5.20 | 0.13 | 2.5% |
| High | 15.60 | 0.13 | 0.8% |
Where the CV is used
| Use | How the CV enters |
|---|---|
| Sigma metric | σ = (TEa% − |bias%|) ÷ CV%. The CV is the denominator, so it drives the whole result |
| Reference change value | RCV = √2 × Z × √(CVa² + CVi²), where CVa is this figure |
| Method verification | CLSI EP15 compares an observed CV with the manufacturer’s claim before a method goes live |
| Setting QC limits | Control limits are drawn at multiples of the SD, so an SD estimated from too few points produces limits that are wrong in both directions |
| Comparing analysers | The only fair comparison between two instruments measuring at different concentrations |
Why an SD alone tells you nothing
A standard deviation of 0.13 mmol/L is neither good nor bad. It becomes one or the other only when you know what it is a deviation from. Around a mean of 5.20 mmol/L it is a coefficient of variation of 2.5%, which is respectable for glucose. Around a mean of 2.60 mmol/L — the same instrument, the same scatter, a lower control — it is 5.0%, twice the relative imprecision. Dividing the SD by the mean and multiplying by a hundred removes the units and makes the figure comparable: between levels, between analytes, between instruments and between laboratories.
That comparability is why the CV, and not the SD, is the currency of laboratory quality. The sigma metric divides allowable total error by it. The reference change value combines it with biological variation to decide whether a patient has really changed. Method verification under CLSI EP15 compares an observed CV against the manufacturer’s claim. Each of those calculations would be meaningless with a bare SD, because none of them knows what concentration it came from.
Two practical points about calculating one. The first is how much data it takes: an SD from five results is little more than a guess, twenty is the usual minimum, and a month of routine QC is better still. Control limits drawn from an unstable SD are wrong in both directions at once — too tight, and the run is rejected for nothing; too wide, and real error passes unnoticed. The second is that the CV must always be quoted with its concentration. Imprecision is generally worse at the bottom of the measuring range, so a figure from a high control says very little about performance at a decision limit sitting near the detection limit.
Finally, judge the CV against a goal rather than against a general sense of what looks small. The goal should come from somewhere defensible — a biological-variation-derived specification, a regulatory allowable total error, or a scheme’s own limits — and it differs by an order of magnitude between analytes. A CV of 4% would be entirely acceptable for creatinine and unacceptable for sodium, where the clinically important differences are far smaller than the number itself suggests.
Frequently asked questions
How do you calculate the coefficient of variation?
Divide the standard deviation by the mean and multiply by 100. An SD of 0.13 around a mean of 5.20 is a CV of 2.5%. Both must come from the same set of measurements and be in the same units, which then cancel.
What is a good CV for a laboratory method?
It depends entirely on the analyte. Under 2% is typical for well-controlled electrolytes, 2–5% covers most routine chemistry, and 5–10% is normal and often acceptable for immunoassays. Compare the figure with a published goal for that analyte rather than with a general rule.
Why is the CV better than the standard deviation?
Because the SD carries the analyte’s units and therefore cannot be compared across analytes or across concentrations. The CV expresses scatter as a percentage of the mean, which cancels the units and makes an SD of 0.13 interpretable.
How many results do I need before the CV is reliable?
At least 20, and preferably a month of routine QC at the level in question. An SD from a handful of points is unstable, and any control limits or sigma metrics derived from it inherit that instability. CLSI EP15 sets out a formal protocol for verifying precision.
Why does the CV differ between QC levels?
Because absolute scatter often stays roughly constant across the measuring range while the mean does not, so the same SD becomes a larger percentage at a lower concentration. It is also genuinely harder to measure small amounts. Always quote the CV with the level it was measured at.
Related calculators
References
- CLSI EP15-A3. User Verification of Precision and Estimation of Bias; Approved Guideline. 3rd ed. Clinical and Laboratory Standards Institute; 2014.
- Westgard JO. Basic QC Practices. 4th ed. Westgard QC; 2016.
- Fraser CG. Biological Variation: From Principles to Practice. AACC Press; 2001 — analytical performance specifications derived from biological variation.
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.