The incompressibility ( compression modulus ) K _ { 0 } of infinite symmetric nuclear matter at saturation density has become one of the major constraints on mean-field models of nuclear many-body systems as well as of models of high density matter in astrophysical objects and heavy-ion collisions .
It is usually extracted from data on the Giant Monopole Resonance ( GMR ) or calculated using theoretical models .
We present a comprehensive re-analysis of recent data on GMR energies in even-even ^ { 112 - 124 } Sn and ^ { 106 , 100 - 116 } Cd and earlier data on 58 \leq A \leq 208 nuclei .
The incompressibility of finite nuclei K _ { A } is calculated from experimental GMR energies and expressed in terms of A ^ { -1 / 3 } and the asymmetry parameter \beta = ( N-Z ) /A as a leptodermous expansion with volume , surface , isospin and Coulomb coefficients K _ { vol } , K _ { surf } , K _ { \tau } and K _ { coul } .
Only data consistent with the scaling approximation , leading to a fast converging leptodermous expansion , with negligible higher-order-term contributions to K _ { A } , were used in the present analysis . Assuming that the volume coefficient K _ { vol } is identified with K _ { 0 } , the K _ { coul } = - ( 5.2 \pm 0.7 ) MeV and the contribution from the curvature term K _ { curv } A ^ { -2 / 3 } in the expansion is neglected , compelling evidence is found for K _ { 0 } to be in the range 250 < K _ { 0 } < 315 MeV , the ratio of the surface and volume coefficients c = K _ { surf } / K _ { vol } to be between -2.4 and -1.6 and K _ { \tau } between -840 and -350 MeV .
In addition , estimation of the volume and surface parts of the isospin coefficient K _ { \tau } , K _ { \tau,v } and K _ { \tau,s } , is presented .

We show that the generally accepted value of K _ { 0 } = ( 240 \pm 20 ) MeV can be obtained from the fits provided c \sim -1 , as predicted by the majority of mean-field models .
However , the fits are significantly improved if c is allowed to vary , leading to a range of K _ { 0 } , extended to higher values .
The results demonstrate the importance of nuclear surface properties in determination of K _ { 0 } from fits to the leptodermous expansion of K _ { A } .

A self-consistent simple ( toy ) model has been developed , which shows that the density dependence of the surface diffuseness of a vibrating nucleus plays a major role in determination of the ratio K _ { surf } / K _ { vol } and yields predictions consistent with our findings .