  In this work, we have constructed a relation between the surface brightness
($\Sigma$) and diameter (D) of Galactic C- and S-type supernova remnants
(SNRs). In order to calibrate the $\Sigma$-D dependence, we have carefully
examined some intrinsic (e.g. explosion energy) and extrinsic (e.g. density of
the ambient medium) properties of the remnants and, taking into account also
the distance values given in the literature, we have adopted distances for some
of the SNRs which have relatively more reliable distance values. These
calibrator SNRs are all C- and S-type SNRs, i.e. F-type SNRs (and S-type SNR
Cas A which has an exceptionally high surface brightness) are excluded. The
Sigma-D relation has 2 slopes with a turning point at D=36.5 pc: $\Sigma$(at 1
GHz)=8.4$^{+19.5}_{-6.3}$$\times10^{-12}$ D$^{{-5.99}^{+0.38}_{-0.33}}$
Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ (for $\Sigma$$\le3.7\times10^{-21}$
Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ and D$\ge$36.5 pc) and $\Sigma$(at 1
GHz)=2.7$^{+2.1}_{-1.4}$$\times$ 10$^{-17}$ D$^{{-2.47}^{+0.20}_{-0.16}}$
Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ (for $\Sigma$$>3.7\times10^{-21}$
Wm$^{-2}$Hz$^{-1}$ster$^{-1}$ and D$<$36.5 pc). We discussed the theoretical
basis for the $\Sigma$-D dependence and particularly the reasons for the change
in slope of the relation were stated. Added to this, we have shown the
dependence between the radio luminosity and the diameter which seems to have a
slope close to zero up to about D=36.5 pc. We have also adopted distance and
diameter values for all of the observed Galactic SNRs by examining all the
available distance values presented in the literature together with the
distances found from our $\Sigma$-D relation.
