We present an empirical relation between the cold gas surface density ($Sigma_{rm gas}$) and the optical extinction (${rm A_V}$) in a sample of 103 galaxies from the Extragalactic Database for Galaxy Evolution (EDGE) survey. This survey provides CARMA interferometric CO observations for 126 galaxies included in the Calar Alto Legacy Integral Field Area (CALIFA) survey. The matched, spatially resolved nature of these data sets allows us to derive the $Sigma_{rm gas}$-${rm A_V}$ relation on global, radial, and kpc (spaxel) scales. We determine ${rm A_V}$ from the Balmer decrement (H$alpha$/H$beta$). We find that the best fit for this relation is $Sigma_{rm gas} ({rm M_odot pc^{-2}})sim~26~times~ {rm A_V}({rm mag})$, and that it does not depend on the spatial scale used for the fit. However, the scatter in the fits increases as we probe smaller spatial scales, reflecting the complex relative spatial distributions of stars, gas, and dust. We investigate the $Sigma_{rm gas}$/ ${rm A_V}$ ratio on radial and spaxel scales as a function of ${rm EW(Halpha)}$. We find that at larger values of ${rm EW(Halpha)}$ (i.e., actively star-forming regions) this ratio tend to converge to the value expected for dust-star mixed geometries ($sim$ 30 $mathrm{M_{odot} ,pc^{-2},mag^{-1}}$). On radial scales, we do not find a significant relation between the $Sigma_{rm gas}$/${rm A_V}$ ratio and the ionized gas metallicity. We contrast our estimates of $Sigma_{rm gas}$ using ${rm A_V}$ with compilations in the literature of the gas fraction on global and radial scales as well as with well known scaling relations such as the radial star-formation law and the $Sigma_{rm gas}$-$Sigma_*$ relation. These tests show that optical extinction is a reliable proxy for estimating $Sigma_{rm gas}$ in the absence of direct sub/millimeter observations of the cold gas.
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