Worked example
For 100 mg with standard uncertainty 0.2 mg in a final 50 mL with standard uncertainty 0.1 mL, concentration is 2 mg/mL. Combined standard uncertainty is about 0.005657 mg/mL (0.2828%). With k = 2, expanded uncertainty is about 0.011314 mg/mL.
Enter standard uncertainties, not arbitrary tolerances
A stated limit, instrument resolution or expanded uncertainty cannot automatically be entered as a standard uncertainty. First evaluate the measurement information and its distribution. If a report supplies expanded uncertainty and a coverage factor, those need to be interpreted before use here.
The two inputs must be independent
The formula uses first-order propagation with no covariance term. It is appropriate when relative uncertainties are small and the mass and volume estimates are independent. Correlation, purity, incomplete transfer and other significant contributions need a fuller measurement model.
Coverage factor is an explicit choice
Expanded uncertainty multiplies the combined standard uncertainty by your chosen k. The example value 2 does not guarantee 95% coverage for every situation. This page reports measurement uncertainty only; it does not choose a concentration, dose or administration volume. Use final solution volume, not solvent volume added.
Range of this simplified tool
For a clear, bounded use of the first-order model, this page accepts standard uncertainties up to 10% of each measured input. That is a calculator scope limit, not a universal metrology rule. Smaller input uncertainty does not establish that the entire measurement process has been modeled.
Explore the related calculation
For a different starting point, try the concentration and density guide or return to the main calculator. Browse the complete tool directory for this site.
Reference and corrections
The definitions and assumptions above follow these sources; the examples and calculator arithmetic are original to this page.
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