Computation Error Uncertainty Worksheet Features 
This drill-down worksheet provides a useful tool for evaluating measurement uncertainty due to computation error.

Since computer or calculator precision is limited, each step of a computation generates uncertainty.  These uncertainties propagate through the computation, emerging as part of the result.  In most cases, the use of double-precision arithmetic can reduce computation error uncertainty. However, uncertainty due to round-off or computer truncation can become serious for quantities based on a large number of calculations, such as in iterative processes, calculations involving matrix products or inverses, calculations involving trigonometric or lognormal functions, etc.

Computation errors contribute to the uncertainty in the resulting value in varying degrees.  For example, if the calculated value is the sum of two quantities, the computation error uncertainty is the root sum square (RSS) of the round-off uncertainties for each quantity. However, if the calculated value is the product of two quantities that are multiplied, the computation error uncertainty is the RSS of the second quantity times the round-off error of the first quantity and the first quantity times the round-off error of the second quantity.

The Round-off and Other Computation Errors table of the Computation Error Uncertainty Worksheet allows you to enter up to 30 error sources for estimating the total computation uncertainty.  Brief descriptions of the table entries are given below.

 
Error Source Description

A brief description of the error source is entered into the first column of the table.

Computed or Measured Value
The number entered for the Computed or Measured Value column for an error source can be in any appropriate units. However, care must be taken to ensure that the resulting computation uncertainty for the error source is in the subject parameter nominal or tolerance units that have selected for reporting the uncertainty estimates. Otherwise, a suitable conversion factor must be incorporated in the Source Coefficient.

Approx. No. Calcs
This column is used to enter an estimated number of calculations involved in obtaining the computed or measured value of the error source. 

Decimal Digits
The precision of the device making the calculations is entered in this column.  The precision is stated in decimal digits (i.e. number of digits to the right of the decimal point).

Source Coefficient
This variable relates the error due to computation to the final computed value.

Computation Uncertainty
UncertaintyAnalyzer employs the uniform distribution for estimating the uncertainty due to round-off or other computational error.

Total Computation Uncertainty
The bottom section of the Computation Error Uncertainty Worksheet displays the total uncertainty due to computation error. The total computation uncertainty is obtained by combining the computation uncertainties for the individual error sources in a root-sum-square (RSS) manner.