For an oriented link diagram $D$, the warping degree $d(D)$
is the smallest number of crossing changes which are needed
to obtain a monotone diagram from $D$.
We show that $d(D) + d(-D) + \mathit{sr}(D)$ is less than or equal to
the crossing
number of $D$, where $-D$ denotes the inverse of $D$ and $\mathit{sr}(D)$
denotes the number of components which have at least one self-crossing.
Moreover, we give a necessary and sufficient condition for
the equality. We also consider the minimal
$d(D) + d(-D) + \mathit{sr}(D)$ for all diagrams $D$.
For the warping degree
and linking warping degree, we show some relations to the
linking number, unknotting number, and the splitting number.