The additional dilution factor used in a concentration calculation describes how much a solution was diluted after digestion or extraction and making it up to a defined volume, before measurement. Record it separately from the conversion involving sample mass and final digest volume. That separation makes double counting easier to spot.
A note such as “diluted tenfold, then fivefold for remeasurement” is incomplete: the combined factor depends on which solution was used for the second dilution. Record the source solution, aliquot and final volume at each step. This guide explains the calculations and the records needed when a sample is measured again.
Making 1 mL up to 10 mL gives a tenfold dilution
For a volumetric dilution, use consistent volume units:
Dilution factor = final volume after dilution ÷ volume of solution taken.
If 1 mL is made up to a final volume of 10 mL, the factor is 10 ÷ 1 = 10. “Make up to 10 mL” specifies the final volume; it does not mean “add 10 mL of solvent.” This example assumes that the analyte is not lost. Follow the equipment and preparation steps specified by the actual test method.
If the initial concentration and volume are C₁ and V₁, and the diluted concentration and volume are C₂ and V₂, conservation of analyte gives C₁V₁ = C₂V₂. Hence C₁/C₂ = V₂/V₁.
When µL and mL appear together
For 200 µL made up to 10 mL, first convert 200 µL to 0.200 mL. The factor is 10 ÷ 0.200 = 50. Dividing 10 by 200 without aligning the units gives an incorrect result. Enter 50, not the aliquot volume, in the tool's additional dilution factor field.
Multiply the factors for successive dilutions
Suppose 1 mL is made up to 10 mL. Then 2 mL of that diluted solution is made up to 10 mL.
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| Stage | Preparation | Factor |
|---|---|---|
| First | 1 mL made up to 10 mL | 10 |
| Second | 2 mL of the first solution made up to 10 mL | 5 |
| Combined | 10 × 5 | 50 |
The additional dilution factor is 50. If the measured solution contains 2 µg/L, the solution before these dilutions contained 2 × 50 = 100 µg/L. Adding the factors (10 + 5 = 15) is incorrect.
Distinguish a series from separately prepared solutions
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| Preparation history | Solution measured | Total factor |
|---|---|---|
| Original solution → tenfold dilution → fivefold dilution of that solution | Second-stage solution | 50 |
| Original solution → separate tenfold and fivefold dilutions | Fivefold solution | 5 |
| Original solution → tenfold dilution, then the same solution is measured again | Tenfold solution | 10 |
The chronological phrase “tenfold, then fivefold” does not establish a factor of 50. Check whether the second preparation started from the original solution or the existing dilution.
Keep sample mass and final digest volume separate
Suppose 0.5 g of sample is digested, made up to 50 mL, diluted a further 50-fold and measured at 2 µg/L, without blank correction. The original-sample result is:
2 × 50 × (50 ÷ 1000) ÷ 0.5 = 10 mg/kg.
The first 50 is the additional dilution factor; the second 50 is the final digest volume in mL. The ratio 50 mL/0.5 g is a volume-to-mass conversion, not another dimensionless dilution factor. If your laboratory uses the phrase “sample preparation factor,” confirm what it includes. The tool has separate fields for sample mass and final volume, so its additional dilution field should include only dilution between the final digest and the measured solution.
Check both the result and the dilution history when measuring again
Assume a 0.5 g sample was made up to 50 mL and no blank correction applies. A tenfold dilution reads 10 µg/L. A separately prepared 50-fold dilution reads 2 µg/L.
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| Solution used | Measured concentration (µg/L) | Additional dilution factor | Converted result (mg/kg) |
|---|---|---|---|
| Tenfold dilution | 10 | 10 | 10 |
| 50-fold dilution | 2 | 50 | 10 |
These invented results are mathematically consistent. A lower concentration in the measured solution does not necessarily mean a lower concentration in the original sample. If the reading is changed to 2 µg/L but the old factor of 10 is left in place, the calculated result becomes an incorrect 2 mg/kg. Check the reading and its preparation history together, and record which measurement was adopted.
Both measurements came from the same prepared sample. Do not count them as two independently weighed and prepared samples in the tool's n independent samples function. Convert and compare each measurement separately.
Check what concentration the instrument reports
Determine whether each output column represents concentration in the measured solution, concentration after dilution correction, or concentration in the original sample. Entering a value that the instrument has already corrected for dilution, then applying the same factor in the tool, corrects it twice.
The tool expects the concentration in the measured solution before dilution correction. If the relevant output column is uncertain, check the instrument configuration and test records instead of guessing from the magnitude of the result. Also verify whether the factor entered in the instrument actually affects that particular output column; merely seeing a factor on screen does not mean every reported value has been corrected.
Estimate how much dilution is needed
A dilution calculation can help estimate whether the measured solution will fall within the calibration range. If the solution before additional dilution is estimated at 120 µg/L and an illustrative target is 12 µg/L, the required factor is 120 ÷ 12 = 10. The target of 12 µg/L is not a recommendation. In practice, use the calibration range, required concentration level, feasible aliquot and test-method conditions. The tool does not design dilution steps automatically.
The equivalent concentration in the original sample also rises with the additional dilution factor. For a 0.5 g sample made up to 50 mL, a measured-solution concentration of 0.1 µg/L corresponds to 0.1 mg/kg at D = 10, but 0.5 mg/kg at D = 50. This calculation alone does not establish a limit of quantitation. It does show why increasing dilution can affect the sample concentration level you need to measure.
Tool input and a reproducible record
Enter 1 for no additional dilution, or 50 for the two-stage example above. The current tool does not calculate each stage automatically. Retain aliquot volumes, final volumes and the combined factor in the test record. For multiple independently prepared samples, the tool can copy sample 1's final volume, additional factor and blank value; edit any sample prepared under different conditions and verify the inputs shown with its result.
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| Record item | Example entry |
|---|---|
| Prepared solution | Sample A digest made up to 50 mL |
| First dilution | 1.00 mL of digest made up to 10.00 mL; solution A1 |
| Second dilution | 2.00 mL of A1 made up to 10.00 mL; solution A2 |
| Solution measured | A2 |
| Combined additional factor | (10.00 ÷ 1.00) × (10.00 ÷ 2.00) = 50 |
| Adopted reading | Concentration in measured A2 before instrument dilution correction |
These solution labels are illustrative. Use a record system that links every aliquot to its source, final solution and adopted reading. The tool does not store preparation histories.
Correct arithmetic does not settle every analytical concern. EPA Method 6020B, section 9.13.1 describes a dilution test for ICP-MS, but its criteria should not be treated as universal for every analysis. If results disagree after correction, first check the calculation and preparation history, then investigate the measurement in line with the method being used.
Related Japanese guides: converting ICP results to mg/kg and common concentration calculation mistakes.
The tool assists with calculations. Confirm final results against the applicable test method, standard and laboratory procedures.