[1] Primary pressure determinations involve the measurement of pressure without recourse to secondary standard materials. These measurements are essential for ensuring the accuracy of pressures measured in gasketed high-pressure devices. In this study, the wavelength of optical fluorescence bands and the density of single crystal Sm-doped yttrium aluminum garnet Y 3 Al 5 O 12 (Sm:YAG) have been calibrated as a primary pressure scale up to 58 GPa. Absolute pressures were obtained by integrating the bulk modulus determined via Brillouin spectroscopy with respect to volumes measured simultaneously by X-ray diffraction. A third-order Birch-Murnaghan equation of state of Sm:YAG yields V 0 = 1735.15(26) Å 3 , K T0 = 185(1.5) GPa, and K`= 4.18(5). The accompanied pressure-induced shifts of the fluorescence lines Y1 and Y2 of Sm:YAG were calibrated to the primary pressure, thus creating a highly accurate fluorescence pressure scale. These shifts are described as P = (A/B) * {[1 + (Δλ/λ 0 )] B À 1} with A = 2089.91(23.04), B = À4.43(1.07) for Y1, and A = 2578.22(48.70), B = À15.38(1.62) for Y2 bands, where Δλ = λ À λ 0 , λ and λ 0 are wavelengths in nanometer at pressure and ambient conditions. The sensitivity in the pressure determination of the Sm:YAG fluorescence shift is 0.32 nm/GPa, which is identical to that of the ruby scale. Sm:YAG can be considered elastically isotropic up to 58 GPa, implying insensitivity of the determined pressure to the crystallographic orientation under nonhydrostatic or quasi-hydrostatic conditions. The Sm:YAG fluorescence shift is apparently also independent of crystallographic orientation, in contrast to that of ruby. Since the Y fluorescence band of Sm:YAG is insensitive to temperature changes, this material is highly suitable for the measurement of pressure at elevated temperatures.