A high precision measurement of the branching fraction of the decay J/ψ → p p̄ η is performed using (10 087 ± 44) × 10⁶ J/ψ events recorded by the {BESIII} detector at the {BEPCII} storage ring. The branching fractions of the two decays J/ψ → p p̄ η(η → γγ) and J/ψ → p p̄ η(η → π⁺ π⁻ π⁰) are measured individually to be B(J/ψ → p p̄ η(η → γγ)) = (1.480 ± 0.001 ± 0.024)×\,10⁻³ and B(J/ψ → p p̄ η(η → π⁺ π⁻ π⁰)) = (1.557 ± 0.003 ± 0.038)×\,10⁻³, where the first uncertainties are statistical and the second systematic. Both results are compatible within their uncorrelated systematic uncertainties. The combined result is B(J/ψ → p p̄ η)=(1.495 ± 0.001 ± 0.023)×\,10⁻³ where the first uncertainty is the combined statistical uncertainty and the second one the combined systematic uncertainty of both analyses, incorporating correlations between them. In addition, the p p̄ threshold region is investigated for a potential threshold enhancement, and no evidence for one is observed.
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