  We prove inequalities that compare the size of an S-regulator with a product
of heights of multiplicatively independent S-units. Our upper bound for the
S-regulator follows from a general upper bound for the determinant of a real
matrix proved by Schinzel. The lower bound for the S-regulator follows from
Minkowski's theorem on successive minima and a volume formula proved by Meyer
and Pajor. We establish similar upper bounds for the relative regulator of an
extension of number fields.
