Enter your replicate measurements to get the relative standard deviation as a percentage, alongside the standard deviation and mean it is built from. The working is shown step by step.
Separate values with commas, spaces, tabs or new lines — paste a column straight from a spreadsheet and it will parse. Decimals and negatives are fine.
The shaded bands are one, two and three standard deviations either side of the mean. 4 of 6 values — 67% — fall inside the innermost band.
Show the working, step by step
What RSD tells you that standard deviation cannot
A standard deviation is an absolute quantity carrying the units of the data, which makes it useless for comparing across scales. Consider two analytical methods:
| Method | Mean | SD | %RSD |
|---|---|---|---|
| Trace metal assay | 0.42 ppm | 0.021 ppm | 5.0% |
| Bulk content assay | 250 mg | 2.5 mg | 1.0% |
The bulk assay has a standard deviation more than a hundred times larger, and yet it is the considerably more precise method. Only the RSD makes that visible, because it measures spread as a proportion of what is being measured.
The formula
%RSD = 100 × s / |x̄|
where s is the sample standard deviation and x̄ the sample mean. The
absolute value on the mean keeps the result positive; some sources omit it and report a
signed RSD, though a negative mean is a sign that RSD is the wrong statistic for the data
in the first place.
Analytical work almost always uses the sample standard deviation here, since replicate measurements are a sample of what the method would produce on repetition. That is the default above.
A worked example
Six replicate injections give 10.12, 10.08, 10.21, 10.15, 10.05, 10.18 mg/mL.
- Sum = 60.79 over n = 6, so the mean is 10.1317 mg/mL.
- The squared deviations sum to Σ(x − x̄)² = 0.0182833.
- Dividing by n − 1 = 5 gives a variance of 0.00365667, so s = 0.0604704 mg/mL.
- %RSD = 100 × 0.0604704 ÷ 10.1317 = 0.5968%.
Against a 2% acceptance criterion, this set passes comfortably. Those exact numbers are loaded into the calculator above — open the working to see each squared deviation.
RSD, CV, and what to call it
Relative standard deviation and coefficient of variation are the same calculation. Which name you meet depends on the field:
- %RSD — analytical chemistry, pharmacopoeial methods, quality control, metrology.
- CV — statistics, epidemiology, finance, laboratory medicine.
- CV% — a common hybrid, identical to %RSD.
There is one genuine distinction worth knowing: some laboratory standards separate repeatability RSD (same analyst, same instrument, same day) from reproducibility RSD (varying those factors). The arithmetic is identical; what differs is which sources of variation the replicates were allowed to contain.
When not to use RSD
- The mean is at or near zero. The ratio becomes unstable and then undefined.
- The scale is interval, not ratio. Temperature in °C or °F has an arbitrary zero, so a percentage of the mean is meaningless. Convert to kelvin first, or use the plain standard deviation.
- The data can be negative. Returns, deviations from a target, and differences all fail the ratio-scale requirement.
- The sample is tiny. With n = 3, the RSD is itself estimated so imprecisely that comparing two values of it is rarely justified.
Related calculators
-
Coefficient of variation
The same statistic, reported as a ratio rather than a percentage.
-
Standard deviation calculator
The absolute spread that RSD is built from.
-
Pooled SD
Combining precision estimates across several runs or batches.
-
Standard error
How precisely the mean itself is known.
Common questions
What is relative standard deviation?
The relative standard deviation (RSD) is the standard deviation expressed as a
percentage of the mean: %RSD = 100 × s / |x̄|. Because the units cancel, it is
a pure number, which lets you compare the consistency of measurements taken on completely
different scales.
It is the same quantity as the coefficient of variation. RSD is the name used in analytical chemistry and quality control; CV is the name used in statistics and finance.
What is a good %RSD?
It depends entirely on what is being measured, and the threshold is usually set by a method or a regulator rather than by statistics.
- Analytical chemistry replicate injections: typically ≤ 2%.
- Bioanalytical assays: commonly ≤ 15%, relaxed to ≤ 20% near the lower limit of quantification.
- Manufacturing content uniformity: often ≤ 5%.
Treat any single number you read online as a starting point, not an answer — check the specification for your own method.
Is RSD the same as the coefficient of variation?
Yes, with one wrinkle of convention: RSD is nearly always quoted as a percentage, while the coefficient of variation is often left as a plain ratio. A CV of 0.08 and an RSD of 8% are the same thing. This calculator reports both.
Why does RSD break down when the mean is near zero?
Because the mean is in the denominator. As it approaches zero the ratio explodes towards infinity, and the number stops carrying any useful meaning. If the mean is exactly zero the RSD is undefined and this calculator will say so.
RSD is only meaningful for data on a ratio scale with a genuine, meaningful zero — mass, concentration, count, elapsed time. It is not appropriate for temperature in °C, or for any quantity that can legitimately be negative.
How do I calculate RSD in Excel?
There is no built-in RSD function. Divide the standard deviation by the mean and multiply by 100:
=STDEV.S(A1:A10)/AVERAGE(A1:A10)*100
Use STDEV.P instead if the values are a complete population. Wrap the mean
in ABS() if it could be negative.