Proper scaling in turbulent planar plumes is investigated here using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity Uref=Uctr, and a proper temperature scale for the temperature excess is Θref=Tctr−T∞, where Tctr is the plume centerline temperature and T∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is Vref=(dδ/dx)Uctr, where dδ/dx is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is Rvu,ref=UctrVref=(dδ/dx)Uctr2, a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is Rvθ,ref=VrefΘctr, a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri=defgβΘctrδt/(UctrVref)≈1/2, where g is the gravitational acceleration, β is the thermal expansion coefficient, and δt is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.