A neutron spectrometer, called a magnetic recoil spectrometer (MRS), has been built and implemented at the OMEGA laser facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] for absolute measurements of the neutron spectrum in the range of 6-30 MeV, from which fuel areal density (rhoR), ion temperature (T(i)), and yield (Y(n)) can be determined. The results from the first MRS measurements of the absolute neutron spectrum are presented. In addition, measuring rhoR at the National Ignition Facility (NIF) [G. H. Miller et al., Nucl. Fusion 44, S228 (2004)] will be essential for assessing implosion performance during all stages of development from surrogate implosions to cryogenic fizzles to ignited implosions. To accomplish this, we are also developing an MRS for the NIF. As much of the research and development and instrument optimization of the MRS at OMEGA are directly applicable to the MRS at the NIF, a description of the design and characterization of the MRS on the NIF is discussed as well.