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The model in which Primordial Black Holes (PBHs) constitute a non-negligiblefraction of the dark matter has (re)gained popularity after the firstdetections of binary black hole mergers. Most of the observational constraintsto date have been derived assuming a single mass for all the PBHs, althoughsome more recent works tried to generalize constraints to the case of extendedmass functions. Here we derive a general methodology to obtain constraints forany PBH Extended Mass Distribution (EMD) and any observables in the desiredmass range. Starting from those obtained for a monochromatic distribution, weconvert them into constraints for EMDs by using an equivalent, effective mass$M_{\rm eq}$ that depends on the specific observable. We highlight how limitsof validity of the PBH modelling affect the EMD parameter space. Finally, wepresent converted constraints on the total abundance of PBH from microlensing,stellar distribution in ultra-faint dwarf galaxies and CMB accretion forLognormal and Power Law mass distributions, finding that EMD constraints aregenerally stronger than monochromatic ones.

Primordial Black Holes as Dark Matter: Converting Constraints from Monochromatic to Extended Mass Distributions