Calculate spike addition volume, final fortification, and matrix-spike recovery from matched laboratory preparation and result values.
Table of contents
How to use our Matrix Spike Volume, Recovery and Final Fortification Calculator
- Choose the Concentration unit used by your standard record, method, and instrument results.
- Enter the Sample aliquot volume, Spike solution concentration, and Target final fortification from the preparation worksheet and method.
- Enter the matched Unspiked sample result and Spiked sample result in the same concentration unit.
- Open Advanced options only if you want to enter both Lower recovery limit (%) and Upper recovery limit (%) from your method or SOP.
- Select Calculate, then check that the Theoretical final fortification matches the target and that the Recovery calculation used fits the spike solution share shown.
Definitions
Matrix spike: A sample aliquot with a known amount of analyte added before the applicable preparation and measurement steps.
Spike solution concentration: The concentration of the stock solution used for the addition.
Target final fortification: The planned concentration contributed by the spike in the final combined sample and spike volume.
Unspiked sample result: The measured concentration in the matched aliquot that did not receive spike solution. It estimates the original background.
Spiked sample result: The measured concentration in the matched aliquot after spike addition.
Matrix-spike recovery: The measured added-analyte contribution divided by the theoretical final fortification, expressed as a percent.
Volume correction: Scaling the unspiked background by the original sample's share of final prepared volume before calculating recovery.
Method limits: Lower and upper recovery boundaries set by the applicable method, SOP, or laboratory study.
Common mistakes and quick fixes
Mistake: Entering the stock value in Target final fortification.
Fix: Use Spike solution concentration for the standard strength and Target final fortification for the desired added concentration in the final preparation.
Mistake: Mixing mg/L and ug/L between Spike solution concentration, Unspiked sample result, and Spiked sample result.
Fix: Choose one Concentration unit and enter every concentration in that unit. Change the unit selector before entering values when possible.
Mistake: Using the total bottle or extract volume as Sample aliquot volume.
Fix: Enter only the matrix sample volume present before spike addition.
Mistake: Copying an unpaired result into Unspiked sample result.
Fix: Use the result from the matched unspiked aliquot for the same sample and preparation workflow.
Mistake: Entering only Lower recovery limit (%) or only Upper recovery limit (%).
Fix: Enter both limits from the same method or SOP, or leave both fields blank.
Mistake: Treating Method-limit check as a universal pass or fail rule.
Fix: Enter the recovery limits that apply to your method, analyte, matrix, and laboratory procedure.
Limitations & Key Assumptions / Boundary Conditions
- The calculation assumes the sample aliquot and added spike solution volumes are additive and that no separate final-volume adjustment is made.
- It assumes the unspiked and spiked results are matched aliquots with comparable preparation, measurement, and reporting units.
- The calculator applies volume-corrected recovery only when the spike solution is more than 1% of the final prepared volume. Exactly 1% uses direct recovery.
- Recovery can be negative when the spiked result is below the applicable background contribution. The calculator keeps that value because it may reveal a preparation, measurement, or data-entry issue.
- The Method-limit check compares only with the two limits entered. It does not verify method compliance, holding times, calibration, contamination controls, or data qualifiers.
- This workflow is for a matrix spike based on the stated aliquot and addition. A post-preparation or post-digestion spike can require a different interpretation.
Methodology
Preparation calculation
The calculator solves for the spike-solution volume that produces the requested Target final fortification after the spike solution is mixed with the Sample aliquot volume. The Spike solution concentration must be greater than the target.
required_spike_volume_uL = 1000 * target_fortification * sample_volume_mL / (stock_concentration - target_fortification)
The factor 1000 converts mL to uL. Final prepared volume is the original aliquot plus the calculated addition.
final_prepared_volume_mL = sample_volume_mL + required_spike_volume_uL / 1000
theoretical_final_fortification = stock_concentration * (required_spike_volume_uL / 1000) / final_prepared_volume_mL
Recovery calculation
Direct recovery subtracts the full Unspiked sample result from the Spiked sample result, then divides by the theoretical final fortification.
direct_recovery_pct = 100 * (spiked_result - unspiked_result) / theoretical_final_fortification
When the spike solution share is greater than 1% of final prepared volume, the calculator scales the unspiked background to account for dilution by the added solution.
volume_corrected_recovery_pct = 100 * (spiked_result - unspiked_result * sample_volume_mL / final_prepared_volume_mL) / theoretical_final_fortification
spike_solution_share_pct = 100 * (required_spike_volume_uL / 1000) / final_prepared_volume_mL
The primary Matrix-spike recovery is direct recovery at 1% or less and volume-corrected recovery above 1%. If both recovery limits are entered, the check is inside limits when the selected recovery is greater than or equal to the lower limit and less than or equal to the upper limit.
Worked example
For a 100 mL aliquot, 1,000 ug/L stock, and 20 ug/L target, the required addition is 2,040.816 uL. The final volume is 102.041 mL, so the spike solution share is 2%. With an Unspiked sample result of 5 ug/L and a Spiked sample result of 23.8 ug/L, volume-corrected recovery is 94.5%.