We report on calorimetry under applied hydrostatic pressure and magnetic field at the antiferromagnetic (AFM)-ferromagnetic (FM) transition of Fe$_{49}$Rh$_{51}$. Results demonstrate the existence of a giant barocaloric effect in this alloy, a new functional property that adds to the magnetocaloric and elastocaloric effects previously reported for this alloy. All caloric effects originate from the AFM/FM transition which encompasses changes in volume, magnetization and entropy. The strong sensitivity of the transition temperatures to both hydrostatic pressure and magnetic field confers to this alloy outstanding values for the barocaloric and magnetocaloric strengths ($|Delta S|$/$Delta p$ $sim$ 12 J kg$^{-1}$ K $^{-1}$ kbar$^{-1}$ and $|Delta S|$/$mu_0Delta H$ $sim$ 12 J kg$^{-1}$ K$^{-1}$ T$^{-1}$). Both barocaloric and magnetocaloric effects have been found to be reproducible upon pressure and magnetic field cycling. Such a good reproducibility and the large caloric strengths make Fe-Rh alloys particularly appealing for solid-state cooling technologies at weak external stimuli.
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