I asses the feasibility of multi-variate scaling relationships to estimate glacier volume from glacier inventory data. I calibrate scaling laws against volume observations of optimized towards the purpose of estimating the total global ice volume. This is applied individually to each record in the Randolph Glacier Inventory which is the first globally complete inventory of glaciers and ice caps. I estimate that the total volume of all glaciers in the world is 0.35 ± 0.07 m sea level equivalent. This is substantially less than a recent state-of-the-art estimate. Area volume scaling bias issues for large ice masses, and incomplete inventory data are offered as explanations for the difference.