We study the spatial distribution of the density of states (DOS) at zero bias N(r) in the mixed state of single and multigap superconductors. We provide an analytic expression for N(r) based on deGennes' relationship between DOS and the order parameter that reproduces well scanning tunneling microscopy (STM) data in several superconducting materials. In the single gap superconductor β-Bi2Pd, we find that N(r) is governed by a length scale ξH = √φ0/2πH, which decreases in rising fields. The vortex core size C, defined via the slope of the order parameter at the vortex center, C ∝ (d%/dr|r→0)−1, differs from ξH by a material dependent numerical factor. The new data on the tunneling conductance and vortex lattice of the 2H-NbSe1.8S0.2 show the in-plane isotropic vortices, suggesting that substitutional scattering removes the in-plane anisotropy found in the two-gap superconductor 2H-NbSe2. We fit the tunneling conductance of 2H-NbSe1.8S0.2 to a two gap model and calculate the vortex core size C for each band. We find that C is field independent and has the same value for both bands. We also analyze the two-band superconductor 2H-NbS2 and find the same result. We conclude that, independently of the magnetic field induced variation of the order parameter values in both bands, the spatial variation of the order parameter close to the vortex core is the same for all bands.