The configuration of the three neutrino masses can take two forms , known as the normal and inverted hierarchies . We compute the Bayesian evidence associated with these two hierarchies . Previous studies found a mild preference for the normal hierarchy , and this was driven by the asymmetric manner in which cosmological data has confined the available parameter space . Here we identify the presence of a second asymmetry , which is imposed by data from neutrino oscillations . By combining constraints on the squared-mass splittings [ [ 2 ] ] with the limit on the sum of neutrino masses of \Sigma m _ { \nu } < 0.13 eV [ [ 3 ] ] , and using a minimally informative prior on the masses , we infer odds of 42:1 in favour of the normal hierarchy , which is classified as “ strong ” in the Jeffreys ’ scale . We explore how these odds may evolve in light of higher precision cosmological data , and discuss the implications of this finding with regards to the nature of neutrinos . Finally the individual masses are inferred to be m _ { 1 } = 3.80 ^ { +26.2 } _ { -3.73 } \text { meV } ;m _ { 2 } = 8.8 ^ { +18 } _ { -1.2 } \text { meV } ;m _ { 3 % } = 50.4 ^ { +5.8 } _ { -1.2 } \text { meV } ( 95 \% credible intervals ) .