Understanding how the tropical circulation responds to warming is crucial if we are to project future hydroclimate changes. The net upwards mass flux in tropical convection, termed the "convective mass flux", is the most basic and fundamental quantity used to measure the strength of the tropical circulation. Previous work by Held and Soden (2006) proposed a scaling for changes in the convective mass flux at cloud base. We show, using an ensemble of cloud-resolving simulations, that this constraint does not hold, consistent with previous findings in the literature. We then present a new scaling for changes in convective mass flux based off the clear-sky energy budget which holds throughout the free-troposphere (as opposed to just at cloud base). We then verify this scaling works across a hierarchy of models, from idealized radiative-convective equilibrium simulations to global storm-resolving runs with GFDL's xSHiELD model. This work provides, for the first time, a constraint on changes in convective mass flux which can be derived from first principles, and which is verified across a wide hierarchy of models.