The observation of gravitational-wave signals from merging black-hole binaries enables direct measurement of the properties of the black holes. An individual observation allows measurement of the black-hole masses, but only limited information about either the magnitude or orientation of the black hole spins is available, primarily due to the degeneracy between measurements of spin and binary mass ratio. Using the first six black-hole merger observations, we are able to constrain the distribution of black-hole spins. We perform model selection between a set of models with different spin population models combined with a power-law mass distribution to make inferences about the spin distribution. We assume a fixed power-law mass distribution on the black holes, which is supported by the data and provides a realistic distribution of binary mass-ratio. This allows us to accurately account for selection effects due to variations in the signal amplitude with spin magnitude, and provides an improved inference on the spin distribution. We conclude that the first six LIGO and Virgo observations (Abbott et al. 2016a, 2017a,b,c) disfavour highly spinning black holes against low spins by an odds-ratio of 15:1; thus providing strong constraints on spin magnitudes from gravitational-wave observations. Furthermore, we are able to rule out a population of binaries with completely aligned spins, even when the spins of the individual black holes are low, at an odds ratio of 22,000:1, significantly strengthening earlier evidence against aligned spins (Farr et al. 2017). These results provide important information that will aid in our understanding on the formation processes of black-holes.
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