The direct detection of gravitational waves 1-4 from merging binary black holes opens up a window into the environments in which binary black holes form. One signature of such environments is the angular distribution of the black hole spins. Binary systems that formed through dynamical interactions between alreadycompact objects are expected to have isotropic spin orientations [5][6][7][8][9] (that is, the spins of the black holes are randomly oriented with respect to the orbit of the binary system), whereas those that formed from pairs of stars born together are more likely to have spins that are preferentially aligned with the orbit [10][11][12][13][14] . The bestmeasured combination of spin parameters 3,4 for each of the four likely binary black hole detections GW150914, LVT151012, GW151226 and GW170104 is the 'effective' spin. Here we report that, if the magnitudes of the black hole spins are allowed to extend to high values, the effective spins for these systems indicate a 0.015 odds ratio against an aligned angular distribution compared to an isotropic one. When considering the effect of ten additional detections 15 , this odds ratio decreases to 2.9 × 10 −7 against alignment. The existing preference for either an isotropic spin distribution or low spin magnitudes for the observed systems will be confirmed (or overturned) confidently in the near future.After the detection of a merging binary black hole system, parameter estimation tools compare model gravitational waveforms against the observed data to obtain a posterior distribution on the parameters that describe the compact binary source. The spin parameter with the largest effect on waveforms, and a correspondingly tight constraint from the data 3 , is a mass-weighted combination of the components of the dimensionless spin vectors of the two black holes that are aligned with the orbital axis, referred to as the 'effective spin' − 1 < χ eff < 1 (see Methods section 'Distributions of effective spin and spin magnitude').In Fig. 1 we show an approximation to the posterior inferred on χ eff for the four likely gravitational wave detections GW150914, GW151226, GW170104 and LVT151012 from Advanced LIGO's first and second observing runs (O1 and O2) 3,4 . Because samples drawn from the posterior on χ eff are not publicly released at this time, we have approximated the posterior as a Gaussian distribution with the same mean and 90% credible interval, truncated to − 1 < χ eff < 1. None of the χ eff posteriors is consistent with two black holes with large aligned spins, χ 1,2 0.5; this contrasts with the large spins that are inferred for the majority of black holes in X-ray binaries with spin measurements 16 (see below). The analysis here is relatively insensitive to the precise details of the posterior distributions; other conclusions are more sensitive. In particular, our Gaussian approximation does permit χ eff = 0 for GW151226, whereas the true posterior rules this out at high confidence 2,3 . Small values of χ eff as exhibited in these systems can result fr...