The relative standard deviation (RSD) puts spread into perspective. A standard deviation of 5 g is tiny for 1 kg bags of flour but enormous for a 10 g sample, so on its own it says little. Dividing by the mean and multiplying by 100 turns it into a percentage that can be compared across scales, units and instruments.
Analytical chemists, pharmacists and quality engineers use RSD (often written %RSD) to judge precision: replicate injections on a chromatograph might be required to have RSD ≤ 2%, and tablet weights or assay results are checked the same way. Investors use the same ratio, under the name coefficient of variation, to compare the risk of assets with different average returns.
RSD uses the absolute value of the mean, so it is always positive; the coefficient of variation shown alongside keeps the sign. RSD only makes sense for ratio-scale data where zero means “none” – lengths, masses, concentrations, counts. For temperatures in °C or °F, where zero is arbitrary, the percentage changes if you change units and should not be used.
How to use the Relative Standard Deviation Calculator
- Enter
- Mean (x̄)
- Standard deviation (s)
- Data
- Data set type
Results update as you type, and everything is calculated in your browser.
How it works
Either enter the mean and standard deviation directly, or paste the data and choose sample or population standard deviation. The calculator divides the SD by the absolute value of the mean and multiplies by 100.
Worked example
Five replicate assays gave 98.2, 101.5, 99.8, 100.4 and 100.9% of label claim. The mean is 100.16 and the sample standard deviation 1.2621, so RSD = 1.2621 ÷ 100.16 × 100 = 1.26% – inside a typical 2% precision limit. For tablets of 250 mg with s = 4 mg, RSD = 1.6%.
When RSD is useful
- Comparing the precision of methods or instruments that work at different levels.
- Checking replicate measurements against a %RSD acceptance limit.
- Comparing the variability of groups with very different means, e.g. weights of apples and pineapples.
- Not for interval scales without a true zero, or for means close to zero.
Inputs explained
| Field | What to enter |
|---|---|
| Enter | Choose one: Mean and standard deviation, Raw data |
| Mean (x̄) | A number |
| Standard deviation (s) | A number |
| Data | A list of numbers separated by commas, spaces or new lines |
| Data set type | Choose one: Sample (divide by n − 1), Population (divide by N) |
What each result means
- Relative standard deviation (RSD) = [Standard deviation]÷abs([Mean])×100
- Coefficient of variation (signed) = [Standard deviation]÷[Mean]
Example values
How the main result changes when Mean changes and everything else stays at the example values above:
| Mean (x̄) | Relative standard deviation (RSD) (%) |
|---|---|
| 125 | 3.2 |
| 187.5 | 2.1333 |
| 250 | 1.6 |
| 312.5 | 1.28 |
| 375 | 1.0667 |
| 500 | 0.8 |
Formula
RSD = s ÷ |x̄| × 100% · CV = s ÷ x̄ (keeps the sign of the mean) · s = √(Σ(x − x̄)² ÷ (n − 1))
Worked example
Inputs — Enter: Mean and standard deviation; Mean (x̄): 250; Standard deviation (s): 4.
Results — Mean = 250; Standard deviation = 4; Relative standard deviation (RSD) = 1.6 %; Coefficient of variation (signed) = 0.016; Precision rating = Very good (1 – 2%, typical assay limit).
Key terms
- Relative standard deviation
- The standard deviation as a percentage of the absolute mean.
- Precision
- How close repeated measurements are to each other.
- Ratio scale
- A scale with a true zero, on which ratios such as "twice as much" make sense.
Frequently asked questions
How do I calculate relative standard deviation?
Divide the standard deviation by the mean and multiply by 100. Tablets averaging 250 mg with s = 4 mg have RSD = 4 ÷ 250 × 100 = 1.6%.
Is RSD the same as the coefficient of variation?
Almost. CV = s ÷ x̄ is often written as a percentage too; RSD uses the absolute value of the mean so it is never negative.
What is an acceptable %RSD?
It depends on the method. Many pharmaceutical procedures require ≤ 2% for system precision, trace analysis may accept 10–20%, and biological assays often more.
Should I use the sample or population standard deviation?
Use the sample SD (n − 1) for replicate measurements – that is what laboratories and Excel's STDEV.S report. Use the population SD only when the data are the whole population.
Why can't I use RSD for temperatures in °C?
Because 0 °C is not "no temperature". The same readings in °F give a different RSD. Use kelvins or report the plain SD instead.
What does a high RSD mean?
That values vary a lot compared with their average – low precision or a very heterogeneous sample.
Which fruit is most consistent: apples 100 ± 5 g or oranges 120 ± 30 g?
Apples: RSD 5% versus 25% for oranges, even though oranges are heavier.