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We present precision calculations of dark radiation in the form of gravitonscoming from Hawking evaporation of spinning primordial black holes (PBHs) inthe early Universe. Our calculation incorporates a careful treatment ofextended spin distributions of a population of PBHs, the PBH reheatingtemperature, and the number of relativistic degrees of freedom. We compare ourprecision results with those existing in the literature, and show constraintson PBHs from current bounds on dark radiation from BBN and the CMB, as well asthe projected sensitivity of CMB Stage 4 experiments. As an application, weconsider the case of PBHs formed during an early matter-dominated era (EMDE).We calculate graviton production from various PBH spin distributions pertinentto EMDEs, and find that PBHs in the entire mass range up to $10^9\,$g will beconstrained by measurements from CMB Stage 4 experiments, assuming PBHs come todominate the Universe prior to Hawking evaporation. We also find that for PBHswith monochromatic spins $a^*>0.81$, all PBH masses in the range $10^{-1}\,{\rmg} < M_{\rm BH} <10^9\,$g will be probed by CMB Stage 4 experiments.

Precision Calculation of Dark Radiation from Spinning Primordial Black Holes and Early Matter Dominated Eras