Calculating Weighing Uncertainty

Dear Raj,

First, determine the linearity for the balance from the calibration certificate. For this example, we will assume ± 0.15 mg for a 4-place balance. Balance manufacturers recommend the use of a rectangular distribution to convert the linearity contribution to a standard uncertainty. Therefore, the balance linearity contribution is 0.15mg/(3)1/2 = 0.09 mg. This contribution may have to be counted twice if the sample is weighed by difference -- once for the tare and once for the gross weight, giving a standard uncertainty that equals (2 x (0.09)2)1/2 = 0.13 mg.

Thusly, a weight of 0.0413 g would have a standard uncertainty of 0.13 mg. Using a coverage factor of 2, an uncertainty of 0.26 mg (that would be rounded to 0.3 mg) would be reported. Using this example, the weight would be reported as 0.0413 grams ± 0.0003 grams and the number of significant figures is 3.

I hope this helps. Please see this our corresponding article, Significant Figures and Uncertainty, for additional help with significant figures and uncertainty calculations.

Serving you in chemistry,
Paul R. Gaines, Ph.D.
CEO of Inorganic Ventures & Fellow Chemist

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