The NIST Reference on Constants, Units and Uncertainty

Fundamental Physical Constants


Units &
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Standard Uncertainty and Relative Standard Uncertainty
The standard uncertainty u(y) of a measurement result y is the estimated standard deviation of y.

    The relative standard uncertainty ur(y) of a measurement result y is defined by ur(y) = u(y)/|y|, where y is not equal to 0.

Meaning of uncertainty
If the probability distribution characterized by the measurement result y and its standard uncertainty u(y) is approximately normal (Gaussian), and u(y) is a reliable estimate of the standard deviation of y, then the interval y u(y) to y + u(y) is expected to encompass approximately 68 % of the distribution of values that could reasonably be attributed to the value of the quantity Y of which y is an estimate. This implies that it is believed with an approximate level of confidence of 68 % that Y is greater than or equal to y - u(y), and is less than or equal to y + u(y), which is commonly written as Y= y ± u(y).

Use of concise notation
If, for example, y = 1 234.567 89 U and u(y) = 0.000 11 U, where U is the unit of y, then Y = (1 234.567 89 ± 0.000 11) U.  A more concise form of this expression, and one that is in common use, is Y = 1 234.567 89(11) U, where it understood that the number in parentheses is the numerical value of the standard uncertainty referred to the corresponding last digits of the quoted result.

Additional information
See Uncertainty of Measurement Results.

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