RSD (relative standard deviation) measures the spread of a set of replicate results relative to their mean: RSD = s / x̄ × 100. RPD (relative percent difference) measures how far apart two results are relative to their average: RPD = |x₁ − x₂| / ((x₁ + x₂) / 2) × 100. Use RPD for duplicate pairs and RSD for three or more replicates.
For a single pair, the two are directly linked: the sample RSD equals RPD / √2. That link, and the confusion it causes when limits are compared, is covered below with worked examples.
The Two Formulas
Relative standard deviation
Here s is the standard deviation of all the replicate results and x̄ is their mean. Laboratory RSD values normally use the sample standard deviation, which divides by n − 1. The What Is Relative Standard Deviation? guide covers the concept in more depth.
Relative percent difference
Here x₁ and x₂ are the two results. The numerator is the absolute difference, and the denominator is the average of the pair. Dividing by the average means neither result is treated as the “true” value.
That design choice separates RPD from percent error, which divides by a reference value, and from a simple percent change, which divides by the first or earlier value.
The US EPA’s SW-846 Chapter One describes the two measures in exactly these terms: RSD is the general precision estimate, and RPD is used “when only two samples are available,” where the two results come from independently prepared aliquots of the same sample or from replicate samples.
RSD vs RPD at a Glance
| Feature | RSD | RPD |
|---|---|---|
| Number of results | Two or more (usually three or more) | Exactly two |
| Based on | Standard deviation of all values | Difference between two values |
| Denominator | Mean of all values | Average of the pair |
| Typical use | Replicate precision, method validation, system suitability | Field or laboratory duplicates, matrix spike duplicates |
| Relationship for n = 2 | RSD = RPD / √2 | RPD = √2 × RSD |
| Maximum value (non-negative data) | No fixed maximum | 200% |
| Can be pooled across many sets | Yes, through pooled variance | Usually converted to an RSD first |
Same Pair, Both Metrics
A soil sample is split and analysed in duplicate for lead. The results are 24.6 mg/kg and 26.2 mg/kg.
RPD: The difference is 1.6 mg/kg and the pair average is 25.4 mg/kg.
RSD: The mean is also 25.4 mg/kg. The deviations are −0.8 and +0.8, so the squared deviations add to 1.28. With the sample divisor, n − 1 = 1:
The same two numbers give 6.30% as an RPD and 4.45% as a sample RSD. Neither is wrong. They are different measures, and the gap between them is exactly the factor √2.
If you used the population standard deviation (dividing by n = 2), the RSD would be 3.15%, exactly half the RPD. That is one reason the sample versus population choice needs to be stated for small data sets.
Why RSD = RPD / √2 for Duplicates
For two values x₁ and x₂, write the difference as d = x₁ − x₂. Each value lies d/2 from the mean, so the sum of squared deviations is 2 × (d/2)² = d²/2. With the sample divisor of 1:
Because the pair mean and the RPD denominator are the same number, the conversion is exact:
- RSD (sample) = RPD / √2 ≈ 0.7071 × RPD
- RPD = √2 × RSD (sample) ≈ 1.4142 × RSD
The EPA states the same identity in a 2013 technical fact sheet on soil subsampling (OSWER 9200.1-117FS): “%RSD and RPD are mathematically interchangeable: %RSD = RPD ÷ √2.” The ITRC glossary makes the complementary point that RPD “is not equal to” the RSD of the same two results. Both statements are true. The two numbers are never equal, but they always differ by the same factor.
| RPD limit | Equivalent sample RSD for a pair |
|---|---|
| 10% | 7.1% |
| 20% | 14.1% |
| 30% | 21.2% |
| 35% | 24.7% |
| 49.5% | 35% |
Comparing a 20% RPD limit directly with a 15% RSD result, as if they were on the same scale, gives the wrong conclusion. Convert one of them first.
Why RPD Does Not Extend to Three or More Results
Add a third result to the lead example: 24.6, 26.2 and 25.1 mg/kg. RPD has no single answer, because there are three possible pairs.
| Pair | RPD |
|---|---|
| 24.6 and 26.2 | 6.30% |
| 24.6 and 25.1 | 2.01% |
| 26.2 and 25.1 | 4.29% |
Picking the largest and smallest values (6.30%) ignores the middle result entirely. Averaging the three RPDs has no standard interpretation either.
RSD handles the set in one step. The mean is 25.3 mg/kg, the sample standard deviation is 0.8185 mg/kg, and the RSD is 3.24%. Every value contributes, and the result can be compared with other replicate sets of any size.
The same logic applies to larger sets. Six replicates of 48.2, 49.5, 47.9, 50.3, 48.8 and 49.1 give a sample RSD of 1.79%. The RPD of the highest and lowest values is 4.89%, a number that depends only on the two extremes and would tend to grow as more replicates are added.
Duplicate Pairs at Different Concentrations
RPD is most often applied to many pairs across a range of sample concentrations. The table shows how the same absolute agreement looks at different levels.
| Duplicate results | Pair mean | RPD | Sample RSD |
|---|---|---|---|
| 102 and 98 | 100 | 4.00% | 2.83% |
| 15.2 and 14.6 | 14.9 | 4.03% | 2.85% |
| 3.10 and 3.12 | 3.11 | 0.64% | 0.45% |
| 0.45 and 0.52 | 0.485 | 14.43% | 10.21% |
The last pair differs by only 0.07 units but has the largest RPD, because its average is small. Near the reporting limit, RPD and RSD both inflate for the same reason RSD does with any small mean.
That is why some programs switch to an absolute criterion at low levels. The EPA’s National Functional Guidelines for inorganic data review (2020) use a 20% RPD limit, or the limit in the project’s quality assurance plan, when both the sample and duplicate are at least five times the quantitation limit (QL). When either result is below 5 × QL, the check becomes whether the absolute difference is within the QL.
Worked example: a batch of duplicates
Suppose a laboratory with a QL of 0.5 mg/L applies that convention, so 5 × QL = 2.5 mg/L:
| Sample | Duplicate | RPD | Both ≥ 2.5? | Criterion used | Result |
|---|---|---|---|---|---|
| 12.4 | 13.1 | 5.49% | Yes | RPD ≤ 20% | Pass |
| 4.35 | 4.12 | 5.43% | Yes | RPD ≤ 20% | Pass |
| 2.61 | 3.38 | 25.71% | Yes | RPD ≤ 20% | Fail |
| 0.62 | 0.95 | 42.04% | No | Difference ≤ 0.5 | Pass (0.33) |
| 8.80 | 11.02 | 22.40% | Yes | RPD ≤ 20% | Fail |
The fourth pair has the highest RPD in the batch but passes, because both results are close to the QL and their absolute difference is small. The two failures would be reviewed for sample heterogeneity, preparation errors or instrument problems. The guidelines also note that a non-detect entered as zero always produces an RPD of 200%, which is one reason low-level pairs need a different rule.
These numbers illustrate one program’s convention. Your limits come from your method, quality assurance project plan or regulator.
When RPD Is the Better Choice
RPD is the natural metric when your quality control design produces pairs:
- Laboratory duplicates: one sample prepared and analysed twice.
- Field duplicates: two samples collected at the same place and time, which include sampling variability as well as analytical variability.
- Matrix spike and matrix spike duplicate (MS/MSD): two spiked portions of a sample. SW-846 notes that precision for organic analyses is usually assessed this way, while laboratory duplicates are more common for inorganic analytes. The EPA’s organic data review guidelines calculate the RPD from percent recoveries rather than concentrations when the two sample amounts differ. Recoveries of 92% and 104% give an RPD of 12.24%.
RPD is quick to calculate for every pair in a batch and easy to compare with a fixed limit. Acceptance limits for RPD are set by the method, the regulatory program or the laboratory. There is no universal RPD limit.
Where more than two results are possible, some programs prefer them. Hawaii’s environmental hazard guidance, for example, recommends field triplicates “wherever feasible” and evaluates precision with RPD only when duplicates are all that can be collected.
When RSD Is the Better Choice
RSD is the better metric whenever you have three or more results that should agree:
- replicate measurements for method precision or repeatability
- replicate injections in a chromatography system suitability test
- control-sample results tracked over time
- any comparison of precision between data sets with different numbers of values
RSD also pools cleanly. Many duplicate pairs can be combined into one precision estimate through their squared relative differences, which is the approach described in the pooled RSD guide.
What RPD Should You Expect From a Known RSD?
If you know a method’s repeatability RSD, you can estimate how far apart duplicates will normally be. The repeatability limit, r = 2.8 × sᵣ, is the difference two results should stay within about 95% of the time. The factor 2.8 is roughly 1.96 × √2, as the Eurachem method validation guide explains.
In relative terms, most duplicate RPDs should stay below about 2.8 times the repeatability RSD. A method with RSDᵣ = 5% should rarely produce duplicate RPDs above about 14%. This is an approximation, because RPD divides by the pair mean rather than the true mean, but it is a useful sanity check when setting an internal RPD limit. The conditions behind repeatability are explained in Repeatability vs Reproducibility RSD.
Strengths and Limitations
| RSD | RPD | |
|---|---|---|
| Strengths | Uses all values; standard in precision statements; can be pooled; works for any n ≥ 2 | Simple; symmetric (neither value is the reference); natural for duplicate QC designs |
| Limitations | Unstable with small n; inflates near a zero mean; needs sample/population choice stated | Only two values; inflates near zero; capped at 200%; not directly comparable with RSD |
Common Mistakes
- Dividing by one of the results. (26.2 − 24.6) / 24.6 × 100 = 6.50%, not 6.30%. That is a percent difference relative to the first result, not an RPD.
- Comparing RPD and RSD values directly. For a pair, RPD is always about 1.41 times the sample RSD. Convert before comparing a result with a limit written in the other metric.
- Using RPD for three or more replicates. Choose RSD instead, or report every pairwise difference if a procedure specifically asks for it.
- Mixing signed and unsigned values. RPD normally uses the absolute difference. Some quality control schemes deliberately keep the sign so they can plot duplicates on a control chart with two-sided limits, as AIHA’s laboratory accreditation guidance describes. Either approach works, but label which one you used and never mix them in one data set.
- Applying percentage limits near zero. When one or both results are close to the detection or reporting limit, a large RPD may reflect the tiny denominator rather than poor precision.
Checking Your Numbers
For any duplicate pair, calculate the RPD, divide it by 1.4142, and compare the result with the sample RSD of the same two values. If the numbers do not match, one of the calculations has an error.
Enter the pair in the RSD Calculator with the Sample (n − 1) option to get the sample RSD directly, then multiply by √2 to check your RPD. For replicate sets of three or more, the calculator’s RSD is the figure to report.
Frequently Asked Questions
Is RPD the same as percent difference?
Not always. Relative percent difference divides the difference between two results by their average, so neither value is treated as the reference. Percent difference or percent error usually divides by one chosen value, such as a reference or expected value. The two give different numbers for the same pair.
Can RPD be used for three or more results?
Not directly. RPD is defined for a pair. With three results there are three possible pairs and three different RPD values. For three or more replicates, use RSD, which uses every value in one calculation.
How do I convert RPD to RSD for duplicates?
For a pair of results, the sample RSD equals RPD divided by the square root of 2, or about 0.707 × RPD. An RPD of 10% corresponds to a sample RSD of about 7.07%. The relationship only holds for exactly two values.
What is an acceptable RPD for duplicates?
It depends on the method and program. As one example, the EPA's 2020 inorganic data review guidelines use a 20% RPD limit, or the project's own limit, when both results are at least five times the quantitation limit, and an absolute-difference check below that. Organic MS/MSD limits come from the quality plan or statement of work. There is no single universal value.
Why can RPD never be more than 200%?
The largest possible difference between two non-negative results occurs when one of them is zero. Then the difference equals the non-zero value and the average is half of it, so RPD = 200%. Values near that limit usually mean one result is near zero or below the reporting limit.
