We have performed a careful analysis of constraints on the neutrino mass from current cosmological data . Combining data from the cosmic microwave background and the 2dF galaxy survey yields an upper limit on the sum of the three neutrino mass eigenstates of \sum m _ { \nu } \leq 3 eV ( 95 % conf . ) , without including additional priors . Including data from SNIa observations , Big Bang nucleosynthesis , and HST Hubble key project data on H _ { 0 } tightens the limit to \sum m _ { \nu } \leq 2.5 eV ( 95 % conf . ) . We also perform a Fisher matrix analysis which illustrates the cosmological parameter degeneracies affecting the determination of \sum m _ { \nu } .