Much effort has been devoted to device and materials engineering to realize nanoscale resistance random access memory (RRAM) for practical applications, but a rational physical basis to be relied on to design scalable devices spanning many length scales is still lacking. In particular, there is no clear criterion for switching control in those RRAM devices in which resistance changes are limited to localized nanoscale filaments that experience concentrated heat, electric current and field. Here, we demonstrate voltage-controlled resistance switching, always at a constant characteristic critical voltage, for macro and nanodevices in both filamentary RRAM and nanometallic RRAM, and the latter switches uniformly and does not require a forming process. As a result, area-scalability can be achieved under a device-area-proportional current compliance for the low resistance state of the filamentary RRAM, and for both the low and high resistance states of the nanometallic RRAM. This finding will help design area-scalable RRAM at the nanoscale. It also establishes an analogy between RRAM and synapses, in which signal transmission is also voltage-controlled.