Spike recovery calculator

Percent recovery from a spiked sample — including the sample your spike dilutes, which is the term a spreadsheet usually drops — and mean recovery with its scatter across the levels of an accuracy study.

The formula

Recovery % = (C_spiked − C_unspiked) / C_added × 100 Spiked by volume, with sample volume V and spike volume Vs: C_added = C_std × Vs / (V + Vs) recovered = C_spiked − C_unspiked × V / (V + Vs)

C_unspiked: analyte measured in the sample before spiking — zero for a fortified blank
C_spiked: analyte measured in the same sample after spiking
C_added: concentration the spike adds, measured in the final solution
C_std: concentration of the spiking standard
%RSD: scatter of the recoveries at one level, relative to their mean

Worked example

One spike, three ways of looking at it

A sample reads 12.4 mg/L. Spiked to add a nominal 10.0 mg/L, it comes back at 21.8 mg/L, so recovery is (21.8 − 12.4) / 10.0 = 94.00%.

Now the same spike done by volume: 1.00 mL of a 500 mg/L standard into 50.0 mL of sample. The spike does not add 10.0 mg/L — it adds 9.804 mg/L, because it dilutes itself into 51.0 mL. The native analyte is diluted too, so what the spike actually recovered is 21.8 − 12.4 × (50.0/51.0) = 9.643, and recovery is 98.36%. Credit the spike with the correctly diluted 9.804 mg/L but forget to dilute the analyte that was already there — use bare 12.4 instead of 12.4 × (50.0/51.0) — and you report 95.88% instead. A spike of 2% of the sample volume moved the answer by two and a half points.

An accuracy study puts that on nine determinations. Against the same 12.4 mg/L background, spikes of 5.0, 10.0 and 20.0 mg/L in triplicate give mean recoveries of 92.67%, 95.00% and 95.50%, with %RSD of 3.297%, 3.795% and 2.399% and a grand mean of 94.39% over n = 9. The bias runs the same way at every level, so it is systematic — a method losing about 5% consistently, which is a different problem from one that averages 100% while swinging ±10%.

Common pitfalls

Recovery near 100% is not accuracy on its own
Read it with the %RSD beside it. A method that recovers 100% on average while individual determinations range from 85% to 115% is not accurate; it is imprecise with a flattering mean. The study above is the opposite case — tight scatter around a consistent 5% loss, which is a bias you can investigate and correct. One number cannot tell those apart, which is why the study mode reports the mean, the %RSD and an interval together.
Your spike dilutes the sample
Adding 1.00 mL of standard to 50.0 mL of sample does not add the standard's concentration — it adds 1/51 of it, and it dilutes the analyte that was already there by 50/51. On the worked example that is the difference between reporting 95.88% and 98.36%. There is no safe threshold to memorise: the term you drop is the unspiked result times the spike fraction, so how much it costs you depends on the spike fraction and on how much native analyte there is relative to the spike together. Above, a 2% spike into a sample already carrying more analyte than the spike adds moved the answer 2.48 points — which is why 1% still moves a four-significant-figure result by over a point. Work it out rather than assuming it away.
A recovery below the quantitation limit means very little
Spiking at a level near or below the LOQ produces recoveries that scatter enormously, because the measurement itself is barely quantitative there. That is a statement about the method's range, not about its accuracy. Establish the quantitation limit first, then spike above it.
Spike at levels the method actually sees
A spike ten times the native content swamps the matrix effect you were trying to measure — the analyte you recover is mostly the spike, in a matrix now mostly diluted by your standard. ICH asks for accuracy across the range the method will be used over, which is the reason the study mode takes several levels rather than one.
Above 100% is not a bonus
Recovery of 115% usually means something else in the matrix is adding signal — a co-eluting peak, an interference, a calibration that does not hold at that level. It is as much a finding as a low recovery, and it will not be fixed by reporting it as “good recovery”.
Decimal commas and thousands separators
Values in the study columns are separated by commas, newlines, tabs and spaces, so a decimal comma cannot also be a decimal point: typing “21,8” reads as two values, not one. Use a dot. Numbers grouped like “1,234,567” are rejected outright and listed as unread rather than guessed at.

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