Quick answer
Relative standard deviation RSD = (s ÷ |x̄|) × 100. For 10, 20 and 30 the sample SD is 10 and the mean 20, so RSD = 50%.
Enter the data and choose sample or population. The calculator returns the RSD.
Related tools: Standard Deviation Calculator: Sample or population standard deviation with variance and mean. Relative Frequency Calculator: Relative frequencies and percentages from counts. Mean Absolute Deviation Calculator: Average distance of values from the mean.
How to use the Relative Standard Deviation Calculator
- Type data set, for example 4, 8, 15, 16, 23, 42.
- Choose data type: Sample (n − 1) and Population (n).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Data set | Text, such as 4, 8, 15, 16, 23, 42 | — |
| Data type | Choose one: Sample (n − 1); Population (n) | Starts at Sample (n − 1) |
Formula and method
Formula
RSD = (s ÷ |x̄|) × 100
IEEE-754 double precision; shown to at most 6 decimal places.
Identical to the coefficient of variation.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Data set = 10, 20, 30; Data type = Sample (n − 1).
| Result | Value |
|---|---|
| Relative standard deviation | 50 % |
The first line is the headline result (relative standard deviation). IEEE-754 double precision; shown to at most 6 decimal places.
Lab precision
In analytical chemistry RSD (also called CV) expresses precision. Repeated measurements with RSD under 2% are considered precise for many assays. A mean of 0 makes it undefined.
Compared with SD
SD of 10 means little by itself; relative to a mean of 20 it's 50%, but relative to a mean of 1,000 it would be 1%. Use RSD to compare variability across different scales.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Data set: entering "5, -5" shows "The mean is 0, so RSD is undefined." beside that field and no result.
Choosing between the Relative Standard Deviation Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Standard Deviation Calculator](/statistics/standard-deviation-calculator/) | data set and data type | Population standard deviation (σ) |
| [Relative Frequency Calculator](/statistics/relative-frequency/) | counts | Relative frequencies |
| [Mean Absolute Deviation Calculator](/statistics/mean-absolute-deviation-calculator/) | data set | Mean absolute deviation |
| [Z-Score Calculator](/statistics/z-score-calculator/) | value, mean and standard deviation | Z-score |
| [Mean Median Mode Range Calculator](/statistics/mean-median-mode-range-calculator/) | data set | Mean |
Background: descriptive statistics
Population statistics divide by n and sample statistics divide by n − 1 (Bessel's correction), because a sample tends to understate variability. Use the population version when your data is every value in the group, and the sample version when it is a subset.
Defaults differ between tools, and so do quartile conventions, which can give slightly different values for small data sets; this page states the method it uses.
Assumptions and limitations
- Mean of 0 is undefined
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for data set to confirm this.
Frequently asked questions
Is RSD the same as CV?
Yes. Relative standard deviation and coefficient of variation are the same measure, SD ÷ |mean| × 100.
What is a good RSD?
Depends on the method.
What about negative means?
Absolute value is used.
What does the Relative Standard Deviation Calculator calculate?
Relative standard deviation (RSD) as a percentage. It returns Relative standard deviation.
What formula does the Relative Standard Deviation Calculator use?
RSD = (s ÷ |x̄|) × 100. Identical to the coefficient of variation.
What do I need to enter in the relative Standard Deviation Calculator?
You enter Data set and Data type.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Mean of 0 is undefined.
What does the “Data type” option change?
It sets how the relative Standard Deviation is worked out. The choices are Sample (n − 1) and Population (n).
What is an example of a relative Standard Deviation result?
With data set 10, 20, 30 and data type Sample (n − 1), the relative standard deviation is 50 %.
Related calculators
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Relative Frequency Calculator — Relative frequencies and percentages from counts.
- Mean Absolute Deviation Calculator — Average distance of values from the mean.
- Z-Score Calculator — Standardize a value using a mean and standard deviation.
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Median Calculator — Median of a data set.
Sources
- Standard statistics definition (e.g. NIST/SEMATECH e-Handbook of Statistical Methods)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.