Pharmaceutical Analysis

Accuracy & % Recovery Calculator

Compare the theoretical (added) amount with the amount found — % recovery, % error and absolute error, or mean recovery, SD and %RSD across replicate trials, with every step shown.

Experiment

Drug / sample name (optional)

Printed on the lab record.

Amount unit

Used for both theoretical and found amounts — no conversion.

Amounts

Theoretical / expected amount

The amount added, labelled or calculated.

Experimental / found amount

The amount your analysis found.

Load an example data set (you can edit every value)

Acceptance range (optional)

Leave blank unless your practical gives limits. Nothing is judged against a range you did not enter.

Lower limit

Enter the limits from your practical or monograph, e.g. 98–102%

Upper limit

Laboratory calculation card

Enter the theoretical and found amounts to calculate % recovery.

% Recovery = (Found amount / Theoretical amount) × 100

% Error = [(Found − Theoretical) / Theoretical] × 100

Absolute error = |Found − Theoretical| · Difference from 100% = |100 − % Recovery|

Mean % recovery x̄ = Σ%Rᵢ / n

SD = √[Σ(xᵢ − x̄)² / (n − 1)] · %RSD = (SD / x̄) × 100

Mean % error = Σ%Eᵢ / n · Mean absolute error = Σ|Foundᵢ − Theoreticalᵢ| / n

xᵢ is each trial's % recovery. SD is the sample standard deviation (divides by n − 1), as for experimental replicates, so it needs at least two trials.

Worked example: spiked recovery at three levels

Illustrative values. To check the accuracy of a UV assay, a placebo blend is spiked with the drug at 80 %, 100 % and 120 % of the working concentration (16, 20 and 24 µg/mL) and each preparation is assayed once. Choose Multiple replicates, set the unit to µg/mL and enter the three trials.

Trial 1 (theoretical → found): 16 → 15.82 µg/mL
Trial 2 (theoretical → found): 20 → 20.14 µg/mL
Trial 3 (theoretical → found): 24 → 23.71 µg/mL
Number of trials (n): 3

% Recovery for each trial = (found / theoretical) × 100
%R₁ = 15.82 / 16 × 100 = 98.875 % %R₂ = 20.14 / 20 × 100 = 100.7 % %R₃ = 23.71 / 24 × 100 = 98.7917 %
Mean % recovery x̄ = Σ%Rᵢ / n
(98.875 + 100.7 + 98.7917) / 3 = 298.367 / 3 = 99.4556 %
Squared deviations (xᵢ − x̄)²
0.337045 + 1.54864 + 0.440748 = 2.32644
Sample SD = √[Σ(xᵢ − x̄)² / (n − 1)]
√(2.32644 / 2) = √1.16322 = 1.07853 %
%RSD = (SD / x̄) × 100
(1.07853 / 99.4556) × 100 = 1.08443 %
Mean % error and mean absolute error
Mean % error = (−1.125 + 0.7 + (−1.20833)) / 3 = −0.54 % Mean absolute error = (0.18 + 0.14 + 0.29) / 3 = 0.2033 µg/mL

Mean recovery 99.46 % · SD 1.079 % · %RSD 1.08 % (n = 3)

On average the method found 0.54 percentage points less than was added (accuracy), and the three recoveries agree with each other to about 1 % RSD (precision). Three single determinations are a teaching set: a formal validation usually asks for more determinations, and whether these figures pass is decided by the acceptance criteria in the validation protocol or monograph — enter those limits in the optional range to check them.

Common mistakes

Calculating recovery from the theoretical amount of the whole batch instead of the amount actually added to that preparation.

Using the population SD (dividing by n) instead of the sample SD (n − 1). For a handful of replicates this understates the spread noticeably.

Treating a good %RSD as proof of accuracy. Replicates can agree closely and still all be biased the same way — check the mean recovery as well.

Entering theoretical and found values in different units (for example mg and µg). This calculator converts nothing, so both columns must already share the unit you selected.

Leaving a blank trial row 'to fill in later'. Every visible row is part of n, so remove rows you did not run.

Quoting a pass or fail without stating the limits. A recovery is only acceptable against criteria from the method protocol or monograph.

Assumptions and limitations

With n = 1 the sample SD and %RSD are undefined; with two or three trials they are rough estimates of precision.

When the theoretical amounts differ between trials (80/100/120 % levels), the mean absolute error averages errors made at different levels — compare trials by % recovery instead.

The calculator describes the data you enter; it does not detect outliers or test whether the bias is statistically significant.

Guide: Accuracy, Precision and Percentage Recovery in Pharmaceutical AnalysisThe concept in full, with practice questions.Percentage Recovery CalculatorFor a single recovery where the amounts are in different units or come from concentration × volume.Calibration Curve CalculatorTo turn each absorbance into the 'found' concentration before entering it here.

References

Harris DC, Lucy CA. Quantitative Chemical Analysis. 10th ed. New York: W. H. Freeman (Macmillan Learning); 2019.
International Council for Harmonisation. ICH Q2(R2): Validation of Analytical Procedures. Step 4, adopted 1 November 2023. Source
United States Pharmacopeia–National Formulary. General Chapter <1225> Validation of Compendial Procedures. Rockville (MD): USP.

Common questions

Your practical manual or the monograph sets the limits — for example 98–102% for many assays, wider for trace or biological methods. Enter them in the optional acceptance range and the calculator will say whether each result lies within them.

Accuracy (mean % recovery, % error) is how close results are to the theoretical value. Precision (SD, %RSD) is how close replicate results are to each other. A method can be precise yet inaccurate if every trial is biased the same way.

More was found than was added. Small excesses can be analytical variation; larger ones usually point to a weighing or dilution error, an interfering substance, or a calculation slip.

The sample standard deviation divides by n − 1, which is zero for a single trial. Enter at least two replicate trials to describe precision.

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy