Coefficient of Variation Calculator

Spread as a share of the mean

A standard deviation of 569 sounds large next to one of 9.47, until you learn that the first comes from salaries around 6,000 and the second from response times around 97. The coefficient of variation, the standard deviation divided by the mean, puts both on the same footing: 9.5% against 9.8%. This calculator returns it for one data set or compares two, works from raw numbers or from a mean and standard deviation you already have, prints the matching Excel formula, adds the small-sample correction and, for two sets, runs the Feltz and Miller test to say whether the difference between the two CVs is real or just noise.

Quick start: paste 2 4 4 4 5 5 7 9, choose Sample, and read 42.8%: a mean of 5.00 and a standard deviation of 2.14.

Raw numbers or a finished mean: the form adapts

What you have - the raw numbers, or a mean and a standard deviation that are already computed, as in a report or a paper.
Data - at least two numbers, separated by spaces, commas or new lines, with no units or thousands separators. A second data set is optional; fill it in to compare, even in different units and sizes.
Sample or population - sample divides by n - 1, like STDEV.S; population divides by n, like STDEV.P, and fits only when you hold every value.
Mean, standard deviation and count - only in the second mode. The count is optional and switches on the small-sample correction.
Read the result - the CV in the headline, then the mean, the standard deviation, the range and the corrected CV; with two sets, both readings side by side and the test.

Five situations, five readings

Salaries against response times. Six monthly salaries, 5,200 to 6,800, and six response times, 82 to 108 ms. The standard deviations, 569.21 and 9.47, point at the salaries; the coefficients, 9.5% and 9.8%, point the other way. The test finds no difference: p = 0.950, so on this evidence neither set varies more relative to its own level.

Two machines filling 500 ml bottles. Ten bottles from each, both averaging 500.00 ml. The first machine stays within 497 to 503 ml, a CV of 0.37%; the second wanders from 492 to 508 ml, 1.03%. With p = 0.004 the difference is very unlikely to be chance, and the second machine needs attention.

Repeat measurements in a lab. Four readings of one sample: 98.2, 101.5, 99.7 and 100.4. The CV, often called the relative standard deviation or %RSD in this setting, is 1.4%. With only four values the small-sample correction lifts it to 1.5%, and the calculator adds a note that so few readings give a rough figure.

Sample or population. For 2, 4, 4, 4, 5, 5, 7, 9 the sample standard deviation is 2.14 and the CV 42.8%; treated as a complete population the standard deviation is exactly 2 and the CV 40.0%. The gap shrinks as the list grows.

Temperatures. Four readings of 32, 41, 50 and 59 °F give 25.5%. The same four readings in Celsius give 86.1%, and in kelvins 2.3%. The table below explains why only the kelvin figure has a meaning.

One set of temperatures, three coefficients

A CV only means something when zero means "none of it", as with money, weight, time or length. Fahrenheit and Celsius put zero at arbitrary points, so the mean, and with it the CV, depends on the scale chosen. Kelvin starts at absolute zero, the only one of the three with a true zero.

Scale	Values	Mean	SD	CV
Fahrenheit	32, 41, 50, 59	45.50	11.62	25.5%
Celsius	0, 5, 10, 15	7.50	6.45	86.1%
Kelvin	273.15 to 288.15	280.650	6.455	2.3%
Takeaway	For temperatures report the standard deviation; if a CV is really needed, only kelvin has a true zero.

Standard deviation or coefficient of variation

Question	Standard deviation	Coefficient of variation
Unit	Same as the data	None, a percentage
Compares sets in different units	No	Yes
Works with negative values or a mean near zero	Yes	No, it becomes meaningless or explodes
Excel formula	=STDEV.S(range)	=STDEV.S(range)/AVERAGE(range)

Short answers on the CV

I only have the mean and the standard deviation. Is that enough?

Yes. Choose the second mode and type them in: a mean of 6,000 with a standard deviation of 569.21 gives 9.5%, the same as the six salaries above. Add the count, 6, and the corrected figure appears, 9.9%.

What is a good coefficient of variation?

There is no universal threshold. A lab assay may be judged against a limit of a few percent, while monthly sales in a small shop can swing far more. Compare the figure with other sets of the same kind, which is what the second data set is for.

Can the CV be more than 100%?

Yes, whenever the standard deviation is larger than the mean, which happens with skewed data such as waiting times. Above 200% the calculator warns that the figure is unstable and suggests the standard deviation or the interquartile range instead.

Is the CV the same as the relative standard deviation?

Yes. Laboratories usually call it %RSD, finance and engineering say coefficient of variation, and both are the standard deviation divided by the mean, times 100%.

Why is there no CV when the mean is zero?

Because the formula divides by the mean. For -2, -1, 0, 1, 2 the calculator gives the standard deviation, 1.58, and explains that the CV does not exist.

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