What is a good relative standard deviation (%RSD)?
There is no single good relative standard deviation. A 2% RSD is the usual expectation for replicate results in a pharmaceutical assay, 15% is acceptable in many bioanalytical methods, and at parts-per-billion levels even 30% can be normal. What matters is the limit set for your method, and how the RSD compares with what similar measurements achieve.
━ Horwitz RSD (%)
How do you calculate %RSD?
%RSD = (s ÷ x̄) × 100
Here s is the sample standard deviation of the replicate results and x̄ is their mean. Take six assay results for one batch of tablets, in mg:
99.2, 100.4, 98.7, 101.1, 100, 99.6
- Mean: the values add to 599, so x̄ = 599 ÷ 6 = 99.8333 mg.
- Sum of squared deviations from the mean: 3.6933.
- Sample SD: s = √(3.6933 ÷ 5) = 0.8595 mg.
- %RSD = 0.8595 ÷ 99.8333 × 100 = 0.86%.
An RSD under 1% for six replicates is good precision for a tablet assay. The RSD calculator does the same steps on your own numbers.
What is a good RSD value in chemistry?
In analytical chemistry the answer depends on what is measured and at what level. Some common reference points:
| Situation | Typical acceptance limit |
|---|---|
| HPLC system suitability, replicate injections of a standard | Often ≤ 2.0% (the monograph sets the exact figure and the number of injections) |
| Assay of a drug substance or product, repeatability | Usually around 1–2% |
| Bioanalytical methods (drug in plasma), FDA and ICH M10 guidance | CV ≤ 15%, ≤ 20% at the lower limit of quantification |
| Trace residues and contaminants (ppm to ppb) | 10–30% or more, judged against the Horwitz value |
These are the usual published ranges, not a substitute for your own procedure. Your SOP, pharmacopoeia monograph or validation protocol sets the limit that applies.
Why is a higher RSD acceptable at low concentrations?
Near the detection limit, a small absolute error is a large fraction of a small result. Horwitz collected thousands of collaborative studies and found that the RSD between laboratories roughly doubles every time the concentration drops by a factor of 100:
RSD (%) = 2^(1 − 0.5 · log₁₀ C)
| Concentration | Horwitz RSD |
|---|---|
| 100% (pure substance) | 2% |
| 1% (10 g/kg) | 4% |
| 0.01% (100 ppm) | 8% |
| 1 ppm (1 mg/kg) | 16% |
| 1 ppb (1 µg/kg) | 45.3% |
Labs use the ratio of their observed RSD to this value (the HorRat) as a sanity check: values between about 0.5 and 2 are usually taken as normal for between-laboratory work.
SD vs RSD: which should you report?
Report the standard deviation when everyone works on the same scale, for example repeat weighings of the same 10 g reference mass. Report the RSD when results differ in size, because it puts precision on a common percentage scale. An SD of 0.5 mg is 0.1% of a 500 mg tablet but 25% of a 2 mg one.
The RSD falls apart when the mean is close to zero, because dividing by a small number inflates it, and it has no meaning for data on an interval scale such as °C, where zero is arbitrary. In those cases report the SD. The same applies to the coefficient of variation, which is the same ratio under another name.
What makes an RSD too high?
If your RSD is above the limit, check for one wild replicate before blaming the method. A single bad injection among six can double the RSD. The outlier calculator shows whether one value stands apart; whether you may exclude it is set by your lab's procedure, not by the statistics. Other usual causes are sample preparation steps that differ between replicates, an unstable baseline and results close to the quantification limit.
Related calculators
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RSD calculator
%RSD from your replicate results, with each step.
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Coefficient of variation calculator
The same ratio under its statistics name.
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Sample vs population SD
Why replicates use n − 1.
Common questions
What is a good %RSD?
It depends on the measurement. For a routine pharmaceutical assay, repeat results within about 2% RSD are the usual expectation; bioanalytical methods in plasma accept up to 15% (20% at the lowest calibrated level); trace analysis at parts per billion can show 20% or more and still be working as expected. Judge an RSD against the limit your method or standard sets, not against one universal number.
How do you calculate %RSD?
%RSD = (s ÷ x̄) × 100, where s is the sample standard deviation and x̄ the mean of the replicate results. For 6 results with a mean of 99.833 and s = 0.8595, %RSD = 0.8595 ÷ 99.833 × 100 = 0.86%.
What is the difference between SD and RSD?
The SD is in the units of the data (mg, mL, seconds); the RSD divides it by the mean and is a percentage. An SD of 0.5 mg is excellent on a 500 mg tablet (0.1% RSD) and poor on a 2 mg one (25% RSD). Use the RSD when you compare precision across different sizes of result.
Is RSD the same as the coefficient of variation?
Yes. RSD and CV are the same ratio, s ÷ x̄. Chemists usually call it %RSD, while biologists, clinical labs and statisticians usually say CV. Both are meaningless when the mean is near zero or when the data can be negative.
Should I use the sample or population SD for RSD?
Use the sample standard deviation (n − 1 in the denominator), because replicates are a sample of what the method could produce. Excel's STDEV.S and the TI-84's Sx give this value.
