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In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or SI system than in others, due to the regular 10-base in all units. Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra.[1][2][3]
Commensurable physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are originally expressed in differing units of measure, e.g. yards and metres, pounds(mass) and kilograms, seconds and years. Incommensurable physical quantities
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