Calculate relative percent difference between two measurements or find the allowed second measurement for a set RPD limit from a reference measurement.
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- Relative Standard Deviation Calculator
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RPD Formula
RPD = |a - b| / ((a + b) / 2) * 100%
- a = first measurement
- b = second measurement
- RPD = relative percent difference, expressed as a percent
For the allowed range mode, the calculator solves the same equation for the second measurement given a reference value x and an RPD limit L:
lower = x * (200 - L) / (200 + L) upper = x * (200 + L) / (200 - L)
RPD is symmetric, so the order of the two measurements does not matter. Both values must be nonnegative and their average must be greater than zero. RPD is undefined when both measurements are zero.
Typical RPD Acceptance Limits
Acceptance limits depend on the method, matrix, and concentration. The values below are common starting points; always defer to your QA plan or method SOP.
| Application | Typical RPD Limit |
|---|---|
| Lab duplicates, aqueous samples | ≤ 20% |
| Lab duplicates, soil/solid samples | ≤ 35% |
| Field duplicates, aqueous | ≤ 30% |
| Field duplicates, soil | ≤ 50% |
| Pharmaceutical assay duplicates | ≤ 2% |
| Results near reporting limit (5x RL) | Often waived or widened |
Quick reference for interpreting a calculated RPD:
| RPD Result | Interpretation |
|---|---|
| 0% – 5% | Excellent agreement |
| 5% – 20% | Acceptable for most environmental work |
| 20% – 50% | Marginal; review near-detection or matrix effects |
| > 50% | Investigate; possible reanalysis required |
Worked Example and FAQ
Example. A duplicate pair reads 12.4 mg/L and 14.1 mg/L.
- Absolute difference: |12.4 − 14.1| = 1.7
- Average: (12.4 + 14.1) / 2 = 13.25
- RPD: 1.7 / 13.25 × 100 = 12.83%
Against a 20% control limit, this pair passes.
How is RPD different from percent difference and percent error? RPD always uses the average of the two values as the denominator, which is why it is "relative." Percent error compares a measured value to a known true value. Percent difference is sometimes used as a synonym for RPD but is also used loosely for other comparisons.
Why use RPD instead of standard deviation? RPD only needs two values, making it the standard precision check for duplicate pairs. With three or more replicates, use relative standard deviation (RSD) instead.
Can RPD exceed 100%? Yes. The maximum is 200%, which occurs when one measurement is zero and the other is positive.
What if a result is below the detection limit? RPD is unstable near the reporting limit. Most QA programs waive the RPD criterion or apply an absolute difference limit when one or both values fall below 5x the reporting limit.
