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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RPD Formula
- 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:
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.
RPD Acceptance Limits
Acceptance limits depend on the method, matrix and concentration. The table gives illustrative program thresholds, not universal limits or recommendations. Use the criterion specified by your QA plan or method SOP.
| Application | Illustrative RPD Limit |
|---|---|
| Lab duplicates, aqueous samples | ≤ 20% |
| Lab duplicates, soil/solid samples | ≤ 35% |
| Field duplicates, aqueous | ≤ 30% |
| Field duplicates, soil | ≤ 50% |
| Assay duplicates (example only) | ≤ 2% |
| Results near reporting limit (5x RL) | Often waived or widened |
Lower RPD indicates closer relative agreement, but RPD alone cannot establish data acceptability or diagnose contamination. Interpret the following ranges only in the context of your prescribed method:
| RPD Result | Interpretation |
|---|---|
| 0% – 5% | Low relative difference; check the method criterion |
| 5% – 20% | Meets a 20% limit only if that limit applies |
| 20% – 50% | Review the method criterion and concentration |
| > 50% | Follow the method’s investigation procedure |
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 compares a duplicate pair. With three or more replicates, relative standard deviation (RSD) may provide a more suitable summary; follow the applicable method.
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 can be unstable near the reporting limit. Follow your method’s specified concentration threshold and its rules for nondetects, absolute differences or alternative precision checks; a universal 5× rule does not apply.
