A circle mapping can approximately reproduce the cross section of magn
etic surfaces and the value of the periodic driving force (K) at a mag
netic island varies with the width of the magnetic island, which sugge
sts the value of K is one of measures for the degradation of magnetic
surfaces. The profile of a rotational transform has flat regions at th
e magnetic islands. The width of the flat region is proportional to th
e width of the magnetic island. Therefore it may be another measure of
the degradation of magnetic surfaces. This method requires less data
for the estimation than the usual method of calculating the width of m
agnetic islands. For collapsed magnetic surfaces that are produced by
overlapping of two magnetic islands, the fractal dimension can effecti
vely estimate the degradation of them. The fractal dimensions of cross
sections of regular magnetic surfaces and clear magnetic islands are
nearly 1, while that of a collapsed magnetic surface is about 1.2 in t
he present study.