We describe new conversion laws, from CO molecular line data to inferred mass column, based on observations of the three main CO isotopologues in several surveys of the Galactic Plane. The new conversion laws replace the use of the single “X-factor” in widespread use, with a more physically-based relationship between the CO line’s optical depth, excitation, and column density. It has the effect of increasing the inferred mass column, over the single X-factor, by typically a factor of 2–3. This means that the molecular mass of the Milky Way may have been substantially underestimated in previous studies, and suggests that scaling laws like the Kennicutt-Schmidt relations may also need to be recalibrated. Because of its statistical basis on a large fraction of our Galaxy’s ISM, this new law is also recommended for use in studies of other Milky-Way-analogue spiral galaxies.