Coefficient Of Variation Calculator
Relative spread: SD as a percentage of the mean — unit-free, so lab precision compares across instruments. Refuses mean = 0 and negative means with the Celsius–Kelvin lesson: relative spread needs an honest zero.
Coefficient Of Variation Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Ratio-scale data only — interval scales with arbitrary zeros (°C) break the ratio
- Sample CV (n − 1 divisor); no CV of the mean variant
In short: Data 12, 9, 15, 11, 8: mean 11, sample SD 2.738613, so the coefficient of variation is 2.738613/11 = 24.896480% — the data’s spread is a quarter of its level, whatever units it came in. That unit-freeness is the whole point: a assay with CV 5% is relatively tighter than one at 25% even when one measures nanograms and the other tonnes. The refusals carry the physics: CV = 0 is division by zero, and a NEGATIVE mean makes the ratio meaningless — the same data in °C and in K produce different CVs, because only one of those scales has an honest zero.
Formula
CV = s / mean × 100%
Sample SD (the n − 1 divisor) over the mean, printed as a percentage. The ratio is a pure number — rescale the units and it does not move, which is exactly why it can compare across instruments.
Worked Example
- Paste your values — measurements on a scale where zero means none.
- Read CV beside its parts: mean and SD printed so the ratio can be audited.
- Use the scale card to sanity-check that your units have an honest zero.
- Compare CVs across instruments or days — that is the measurement-precision use case.
Defaults: mean 11, s 2.738613, CV 24.896480%. Mean = 0 and negative means are refused with the Celsius–Kelvin lesson — relative spread presumes zero means none.
Strengths & Limits Of This Model
Where this engine is strong
- Mean and SD printed beside the ratio so it can be audited
- Scale card makes the honest-zero assumption a visible check, not a hidden one
Where it stops
- No sampling distribution for CV itself (boundary stated)
- Grades nothing — good CVs are field-dependent
Practical Use Cases
Lab QC
assay precision across runs and instruments
Finance
return per unit of risk, unit-free
Operations
relative variability of lead times
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Coefficient Of Variation Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What does CV = 24.896480% actually say?
That the typical spread is about a quarter of the typical level: SD 2.738613 on a mean of 11. It is the SD re-expressed relative to size, so a 12-nanogram assay and a 12-tonne shipment can be compared on even footing — 25% is 25% in either unit.
Why refuse a negative mean?
Because the ratio’s sign flips and its size loses meaning: SD 5 on a mean of −10 gives −50%, a number no decision can consume. The deeper issue is the ZERO: CV presumes the scale’s zero means none of the thing. Temperatures in °C break that; in K they hold — the same readings, different CVs, and only one of them is real.
Why does the page not just use |mean|?
Because a negative mean is not a cosmetic problem the absolute value can patch — it means the scale has no honest zero, and EVERY CV on that scale is an artifact. Refusing names the problem; patching would hide it one decimal at a time.
How is CV different from the SD the stdev page prints?
Divisor and framing: the stdev page prints the raw spread in the data’s units; this page divides it by the mean and prints percent. Same n − 1 sample convention — quote CV when SIZE changes the meaning of spread, quote SD when the units already carry it.
What CV counts as good?
Field-dependent, which is why the page declines to grade it: assay labs often live under 5%, biological data routinely run 20–30%, and some processes sit happily above 50%. The honest comparison is against YOUR baseline — same instrument, same method, before and after.
Can I compare CVs of different variables?
Yes — that is the point. Height in cm against weight in kg, lead times against order sizes: the units divide out. The one thing you cannot do is compare CVs measured on interval scales with arbitrary zeros (°C, year numbers) — the ratio inherits the fake zero.
Does CV have a sampling distribution?
It wobbles like any ratio of estimates, and its SE approximates CV·√((1+2CV²)/n) — out of scope here, stated as a boundary. For most QC uses the running chart of CV values IS the honest interval.
Why n − 1 in the SD?
Same doctrine as everywhere on the site: your data are a sample, the deviations were taken around the sample’s own mean, and the n − 1 divisor unbias the spread before it is standardized. The variance page owns the full argument; this page inherits the convention and says so.