Traditionally, trends of universal turbulence statistics are presented versus Rλ, which is the Reynolds number based on Taylor's scale λ and the root-mean-square (rms) of a component of velocity urms. λ and urms, and hence Rλ, do not have the attribute of universality. The ratio of rms fluid-particle acceleration to the rms of the acceleration caused by the viscous force, Ra, is an alternative to Rλ. Ra is a Reynolds number. It is composed of statistics of the small scales of turbulence. It can be evaluated with single-wire hot-wire anemometry. Like Rλ, it can be partially evaluated by means of flow similarity. Direct measurement of Ra is challenging; therefore, Ra is not a replacement for Rλ. For isotropic turbulence the relationship between Ra and Rλ is given. Anisotropic turbulence is discussed.