Weighing by difference calculates a mass change from recorded before-and-after measurements. The subtraction is simple; the interpretation depends on what was weighed and what else could have changed between the readings.
Name the quantity being calculated
A source container weighed before and after a transfer gives a decrease in its recorded mass. A destination container weighed empty and after receiving material gives an increase. These observations concern different physical boundaries.
NIST Technical Note 1900 includes a weighing-by-differences example and explicitly models the contributions from the containers, balance performance and drift. Its lesson is that the measurement equation and assumptions determine what uncertainty belongs to the result.NIST Technical Note 1900 — Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results (opens in a new tab)
For a routine record, identify which container was measured at each stage and whether its configuration was comparable. A change in cap, label or other weighed component would also contribute to the difference.
A tared display can simplify the visible reading, but the record still needs a clear account of what was included in the tare and what changed afterwards.
Keep source loss separate from destination gain
| Observation | Calculation | Supported description |
|---|---|---|
| Source: 12.3456 g before; 12.3406 g after | 0.0050 g = 5.0 mg decrease | Recorded loss from source assembly |
| Destination: 8.1000 g before; 8.1047 g after | 0.0047 g = 4.7 mg increase | Recorded gain in destination assembly |
| Difference between the changes | 0.3 mg | Unresolved discrepancy requiring context |
The example does not identify where the discrepancy arose. Measurement uncertainty, an unrecorded change or material outside the intended destination are possibilities to investigate, not conclusions established by subtraction.
Reporting “5.0 mg delivered” from the source readings alone would add a recovery claim that was not measured at the destination. The wording should follow the boundary actually observed.
Likewise, a destination mass increase is not a peptide identity or purity measurement. It records mass associated with whatever entered or changed in that weighed assembly.
Do not subtract uncertainty away
For uncorrelated inputs, NIST’s treatment adds their variances when calculating uncertainty in a difference. Shared effects require consideration of correlation rather than automatic use of an independence assumption.NIST Technical Note 1900 — Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results (opens in a new tab)
As a simplified original calculation, two independent readings with standard uncertainty 0.1 mg each give about 0.14 mg standard uncertainty for their difference: the square root of 0.1 squared plus 0.1 squared.
That calculation omits other possible contributions and is not a complete uncertainty budget for a transfer. Its purpose is to show why subtracting two readings does not make their uncertainties vanish.
Make the calculation reconstructable
Preserve the original readings, units, instrument link and event order. State whether the reported quantity represents source loss, destination gain or another explicitly defined change.
If a later correction affects one reading, retain the original and document how the calculated difference changes. A final number without its inputs is difficult to audit or reinterpret.
A useful material record therefore combines arithmetic with a physical description. It lets the reader see what changed, what was actually measured and which transfer or composition assumptions remain unverified.
Sources and further detail
- NIST Technical Note 1900 — Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results (opens in a new tab)
Example E1 and its uncertainty treatment inspected. The article uses original simplified transfer numbers, not the NIST worked dataset or a recommended weighing protocol.
Sources checked 20 September 2026. Numerical examples are hypothetical unless attributed to a study. Measurement explanations are not laboratory protocols or product handling limits. This article has not undergone independent scientific peer review.