© 2016. The American Astronomical Society. All rights reserved. Using the Pan-STARRS1 survey, we derive limiting magnitude, spatial completeness, and density maps that we use to probe the three-dimensional structure and estimate the stellar mass of the so-called Monoceros Ring. The Monoceros Ring is an enormous and complex stellar sub-structure in the outer Milky Way disk. It is most visible across the large Galactic Anticenter region, 120° < l < 240°, -30° < b < +40°. We estimate its stellar mass density profile along every line of sight in 2° × 2° pixels over the entire 30,000 deg2Pan-STARRS1 survey using the previously developed MATCH software. By parsing this distribution into a radially smooth component and the Monoceros Ring, we obtain its mass and distance from the Sun along each relevant line of sight. The Monoceros Ring is significantly closer to us in the south (6 kpc) than in the north (9 kpc). We also create 2D cross-sections parallel to the Galactic plane that show 135° of the Monoceros Ring in the south and 170° of the Monoceros Ring in the north. We show that the northern and southern structures are also roughly concentric circles, suggesting that they may be waves rippling from a common origin. Excluding the Galactic plane ∼±4°, we observe an excess mass of 4 × 106M⊙across 120° < l < 240°. If we interpolate across the Galactic plane, we estimate that this region contains 8×106M⊙. If we assume (somewhat boldly) that the Monoceros Ring is a set of two Galactocentric rings, its total mass is 6×107M⊙. Finally, if we assume that it is a set of two circles centered at a point 4 kpc from the Galactic center in the anti-central direction, as our data suggests, we estimate its mass to be 4 × 107M⊙.