Based on an analytical/numerical modeling approach, this paper details the derivation steps of both in-plane and out-of-plane universal sensitivity expressions of an efficient 3-axis convective accelerometer. The analytical modeling method uses finite element analysis to model the effects of key parameters on the sensitivity of the CMOS micromachined sensor. From the definition of the design space and biasing condition, the heater temperature and key geometric parameters of the sensor are swept in a wide range. Using numerical studies of a previously validated 3D Finite Element Model (FEM), the impact of each specific parameter on sensitivity is then extracted from simulation results. This method is applied to develop both in-plane and out-of-plane sensitivity expressions as a function of main geometrical parameters, which include the height and width of bottom cavity and top cover in addition to the heater temperature. FEM simulations are then used to validate the obtained compact analytical models of the sensitivities for a large range of feasible design parameters through CMOS technology. We obtain a maximum deviation of 9% between numerical and compact model results. Final expressions can be considered as a very useful guide when designing a 3-axis convective accelerometer for an early estimation of sensitivity levels.