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Calculate the coefficient of variation (CV) from your dataset to easily assess relative dispersion and data volatility. Free online statistics calculator.
Separate numbers with spaces, commas, semicolons, or new lines. Please enter at least two numerical values.
Please enter at least two valid numbers to calculate the Coefficient of Variation.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
The coefficient of variation (CV) expresses standard deviation relative to the magnitude of the mean: standard deviation ÷ |mean| × 100%. It is a unitless percentage, which can help compare relative spread when datasets use a meaningful zero and are measured on a ratio scale. It does not make unlike measurements automatically comparable.
This calculator accepts a list of numbers and lets you choose sample or population standard deviation. It reports the count, sum, mean, variance, standard deviation, minimum, maximum, and CV. The default is sample mode and four decimal places. NIST cautions that CV is generally for ratio-scale data and is sensitive when the mean is near zero.
Sample standard deviation: s = √[Σ(xᵢ − x̄)²/(n−1)]
Population standard deviation: σ = √[Σ(xᵢ − μ)²/n]
CV (%) = standard deviation ÷ |mean| × 100
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Separate values with spaces, commas, semicolons, or line breaks. The parser keeps numeric tokens and ignores other text, so compare the displayed count with the values you intended to include.
Choose sample when the observations represent part of a larger group; choose population when they are the complete group being described. The choice changes the standard-deviation denominator and therefore the CV.
Choose from 0 to 10 decimal places; four is the default. This only changes rounding in the display, not the underlying calculation.
For 10, 20, and 30, the mean is 20. The sample standard deviation is 10 and CV is 50%; population standard deviation is about 8.165 and CV about 40.825%. The mode explains the difference.
Use cases
See how the tool fits into real work and everyday tasks.
Compare sample and population modes on the same observations to see how the denominator affects spread, then use the convention required by the assignment.
For ratio-scale measurements such as mass or length, report CV alongside the mean, standard deviation, sample size, and units.
State whether the records are a sample or full population so readers can understand which standard deviation produced the percentage.
Q&A
Find concise answers to common questions and confusing cases.
CV divides by the absolute mean, so a zero mean makes the calculation undefined. A mean close to zero can also make the percentage highly sensitive to small changes.
Usually not as a meaningful relative-spread comparison: Celsius has an arbitrary zero rather than a zero representing absence of temperature. CV is most appropriate for ratio-scale data.
The calculator divides by the absolute value of the mean. That defines the displayed percentage, but negative-valued data may still make CV interpretation inappropriate for the question.
Notes
Review scope, result limitations, and important precautions before use.
A CV is not a universal quality rating, medical threshold, or investment-risk score. Avoid interpreting it when the mean is zero or close to zero, and check whether the variable has a meaningful zero before comparing groups. The calculator’s sample or population setting should reflect how the data were collected, not which result looks preferable.
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