acalculator

What is the coefficient of variation?

Paste a list of numbers. The coefficient of variation calculator divides the standard deviation by the mean and shows the result as a percent (the CV) and as a plain ratio, with the mean and standard deviation it used.

Your numbers

Read as: 10; 12; 23; 23; 16; 23; 21; 16
Data are a
Coefficient of variation (CV)
29.0957%

The coefficient of variation of the 8 values is 29.0957%.

Relative standard deviation (RSD)
29.0957%
CV as a ratio
0.290957
Mean (x̄)
18
Standard deviation (s)
5.237229
Count (n)
8

Coefficient of variation (CV): 29.0957%. The coefficient of variation of the 8 values is 29.0957%.

How to calculate

Computes the coefficient of variation (CV) of a list of numbers, the sample or population standard deviation divided by the mean, as a percent and a ratio.

Example with the default inputs (Data values [10, 12, 23, 23, 16, 23, 21, 16], Data are a Sample (n − 1)): The coefficient of variation of the 8 values is 29.0957%.

Method: CV = s ÷ x̄, shown as 100 × s ÷ x̄ percent; s is the sample (n − 1) or population (N) standard deviation.

  • The CV is meaningful for data on a ratio scale (a true zero), such as lengths, weights or times.
  • The CV is not defined when the mean is 0; near 0 it changes a lot with small changes in the data.
  • A negative mean gives a negative CV; the relative standard deviation uses the size of the mean instead.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Data values 10, 12, 23, 23, 16, 23, 21, 16, Data are a Sample (n − 1) gives Coefficient of variation (CV) 29.095719%, Relative standard deviation (RSD) 29.095719%, CV as a ratio 0.290957, Mean (x̄) 18, Standard deviation (s) 5.237229, Count (n) 8.Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02); NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (s² = Σ(Y − Ȳ)² ÷ (N − 1)), https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm (retrieved 2026-10-02)
  2. Data values 2, 4, 4, 4, 5, 5, 7, 9, Data are a Population (N) gives Coefficient of variation (CV) 40%, CV as a ratio 0.4, Mean (x̄) 5, Standard deviation (s) 2.Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02)
  3. Data values -4, -6, -8, Data are a Sample (n − 1) gives Coefficient of variation (CV) -33.333333%, Relative standard deviation (RSD) 33.333333%, Mean (x̄) -6, Standard deviation (s) 2.Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02)

How it works

For n values x₁ … xₙ:

  • Mean x̄ = (x₁ + … + xₙ) ÷ n
  • Standard deviation s = √(Σ(xᵢ − x̄)² ÷ d), with d = n − 1 for a sample and d = n for a population
  • Coefficient of variation = s ÷ x̄ (the ratio), shown as 100 × s ÷ x̄ percent
  • Relative standard deviation = 100 × s ÷ |x̄| percent (equal to the CV unless the mean is negative)

The values are first divided by a power of two near the largest |x|, which changes no digit, so very large or very small values do not overflow when squared. The ratio does not depend on that scale.

Rules

  • 2 to 1,000 values.
  • When every value is 0, or the mean is 0 (or so close to 0 that the ratio is not a finite number), there is no answer.
  • A mean or standard deviation past the largest double (about 1.8 × 10³⁰⁸) is left out; the CV is still shown.

Output format. The CV and RSD percents and the ratio to 6 significant digits; the mean and standard deviation with up to 6 decimals.

Worked examples by hand

10, 12, 23, 23, 16, 23, 21, 16 as a sample. Sum 144, so x̄ = 18. Deviations −8, −6, 5, 5, −2, 5, 3, −2; squares add to 192. s = √(192 ÷ 7) = 5.237229. CV = 5.237229 ÷ 18 = 0.290957, or 29.0957%.

2, 4, 4, 4, 5, 5, 7, 9 as a population. x̄ = 40 ÷ 8 = 5. Squared deviations 9, 1, 1, 1, 0, 0, 4, 16 add to 32. σ = √(32 ÷ 8) = 2. CV = 2 ÷ 5 = 0.4, or 40%.

−4, −6, −8 as a sample. x̄ = −6, s = √((4 + 0 + 4) ÷ 2) = 2. CV = 2 ÷ −6 = −33.3333%; RSD = 2 ÷ 6 = 33.3333%.

Other questions people ask

What is the coefficient of variation?

The standard deviation divided by the mean, cv = s ÷ x̄. It measures spread relative to the size of the values, so it has no unit. It is often written as a percent: 100 × s ÷ x̄.

How do I calculate the coefficient of variation?

Find the mean, find the standard deviation, and divide. For 10, 12, 23, 23, 16, 23, 21, 16: the mean is 18, the sample standard deviation is 5.2372, and 5.2372 ÷ 18 = 0.29096, or 29.10%.

What is a good coefficient of variation?

There is no single cut-off; it depends on the field. A lower CV means the values sit closer to their mean. Laboratories often set their own limits for repeat measurements, such as a few percent, while biological or sales data can have CVs far above 30%.

Is the coefficient of variation the same as the relative standard deviation?

Nearly. NIST defines the relative standard deviation as 100 × s ÷ |x̄|, the CV as a percent but with the size of the mean. They differ only when the mean is negative, where the CV is negative and the RSD is not.

Should I use the sample or the population standard deviation?

Use the sample one (dividing by n − 1) when your numbers are a sample from a larger group, which is the usual case. Use the population one (dividing by N) only when you have every member of the group.

Why can the CV not be used when the mean is 0?

Dividing by 0 is not defined, and near 0 a tiny change in the mean makes the CV jump. That is why NIST says the CV suits data on a ratio scale, with a true zero and positive values, such as weights or times, and not temperatures in °C.