This topic differs from units of measurement, which see.

Units of measure are the fundamental components of a problem. They are used in many fields to ensure accurate accounting of systems, ideas, and resources.

They are exemplified in problems such as: It takes an orchard owner 3 hours to plant 5 trees. This is expressed mathematically as

3H = 5T.

Simple mathematical arrangement produces

(3/5)H = T

or three-fifths of an hour to plant a tree. If we also include the units in the expression, using the conventions of dimensional analysis we could have written the expression as

3H [hours] = 5T [trees]

Or

T/H = 3/5 [hours/tree], the time budget for planting 1 tree. This gives the orchard owner a way to plan future plantings.

Problems of budgeting and other complex real world problems require units of measure to adequately assess projected outcomes.

For instance a dollar of expenditure on a given program might produce A widgets, B jobs, C unemployment in year 2, D environmental waste, etc.. It is then possible to compare programs on various measures.

When performing a calculation, the selection of the units of measure can be taken to simplify the problem, frequently for the convenience of the researcher or accountant. Thus an astrophysicist might choose to calculate in units of solar masses; an executive for a large business might choose to calculate in millions of dollars; a policy planner might choose to calculate in units of dollars per barrel of oil; an electronic designer might choose to calculate in units of noise level; a web site owner might choose to calculate in units of web page hits per second; a businessman might choose to measure in units of unsold product.

See also

• Stoichiometry
• Intransitivity
• Units of measurement