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Binary populations in young star clusters show multiplicity fractions both lower and up to twice as high as those observed in the Galactic field. We follow the evolution of a population of binary stars in dense and loose star clusters starting with an invariant initial binary population and a formal multiplicity fraction of unity, and demonstrate that these models can explain the observed binary properties in Taurus, Ophiuchus, Chamaeleon, Orion, IC 348, Upper Scorpius A, Praesepe, and the Pleiades. The model needs to consider solely different birth densities for these regions. The evolved theoretical orbital-parameter distributions are highly probable parent distributions for the observed ones. We constrain the birth conditions (stellar mass, M ecl , and half-mass radius, r h ) for the derived progenitors of the star clusters and the overall present-day binary fractions allowed by the present model. The results compare very well with properties of molecular cloud clumps on the verge of star formation. Combining these with previously and independently obtained constraints on the birth densities of globular clusters, we identify a weak stellar mass -half-mass radius correlation for cluster-forming cloud clumps, r h /pc (M ecl /M ) 0.13 0.04 . The ability of the model to reproduce the binary properties in all the investigated young objects, covering present-day densities from 1-10 stars pc -3 (Taurus) to 2 10 4 stars pc -3 (Orion), suggests that environment-dependent dynamical evolution plays an important role in shaping the present-day properties of binary populations in star clusters, and that the initial binary properties may not vary dramatically between different environments.