Checking for errors in calculations and software: Dimensional balance and conformance of units

Although there has always been a general awareness that mathematical expressions must make dimensional sense in terms of the units involved, it is very easy to make simple mistakes in quantitative work that result in profound and potentially dangerous errors. Such errors are ubiquitous in modern research, as can be seen by reviewing government publications where dimensional errors persist despite peer and public review. Software methods have recently become available for checking calculations, equations, algorithms and programs for dimensional soundness. Correctness depends on conformance at two levels: balance of dimensions and agreement among units. Error at either level can now be detected automatically by software. Disagreement among units can even be automatically corrected by software procedures. These software tools can be used to check for errors in calculations and software source code in a way that is similar to using a spelling or grammar checker for text.

Keywords:

• Dimensional analysis
• agreement of units
• quality assurance for calculations and algorithms

Notes

Ferson is one of the developers of Units Calculator, and both it and Dimensional Reasoner are commercially distributed by Applied Biomathematics, which is Ferson's employer. Tel.: [phone]. Fax: [phone]. E‐mail: [email protected].