In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for the value ${\displaystyle u(x_{i})}$ of one index u, occurring at any quantity ${\displaystyle x_{i}}$ of the goods bundle being evaluated, the corresponding value ${\displaystyle v(x_{i})}$ of the other index v satisfies a relationship of the form

${\displaystyle v(x_{i})=au(x_{i})+b\!}$,

for fixed constants a and b. Thus the utility functions themselves are related by

${\displaystyle v(x)=au(x)+b.}$

The two indices differ only with respect to scale and origin. Thus if one is concave, so is the other, in which case there is often said to be diminishing marginal utility.

Thus the use of cardinal utility imposes the assumption that levels of absolute satisfaction exist, so that the magnitudes of increments to satisfaction can be compared across different situations.

In consumer choice theory, ordinal utility with its weaker assumptions is preferred because results that are just as strong can be derived. Cardinal utility shows that the unit we consume can be measured in numbers. It is the less practical form of measuring satisfaction compare to Ordinal utility.