Contemporary FPGA design requires a spectrum of available physical resources. As FPGA logic capacity has grown, locally-accessed FPGA embedded memory blocks have increased in importance. When targeting FPGAs, application designers often specify high-level memory functions which exhibit a range of sizes and control structures. These logical memories must be mapped to FPGA embedded memory resources such that physical design objectives are met. In this work a set of power-efficient logical-to-physical RAM mapping algorithms are described which convert user-defined memory specifications to on-chip FPGA memory block resources. These algorithms minimize RAM dynamic power by evaluating a range of possible embedded memory block mappings and selecting the most power-efficient choice. Our automated approach has been validated with both simulation of power dissipation and measurements of power dissipation on FPGA hardware. A comparison of measured power reductions to values determined via simulation confirms the accuracy of our simulation approach. Our power-aware RAM mapping algorithms have been integrated into a commercial FPGA compiler and tested with 34 large FPGA benchmarks. Through experimentation, we show that, on average, embedded memory dynamic power can be reduced by 26% and overall core dynamic power can be reduced by 6% with a minimal loss (1%) in design performance. Additionally, it is shown that the availability of multiple embedded memory block sizes in an FPGA reduces embedded memory dynamic power by an additional 9.6% by giving more choices to the CAD algorithms.