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ABSTRACT We present updated cosmological constraints from measurements of the gas mass fractions (fgas) of massive, dynamically relaxed galaxy clusters. Our new data set has greater leverage on models of dark energy, thanks to the addition of the Perseus cluster at low redshifts, two new clusters at redshifts z ≳ 1, and significantly longer observations of four clusters at 0.6 < z < 0.9. Our low-redshift (z < 0.16) fgas data, combined with the cosmic baryon fraction measured from the cosmic microwave background (CMB), imply a Hubble constant of h = 0.722 ± 0.067. Combining the full fgas data set with priors on the cosmic baryon density and the Hubble constant, we constrain the dark energy density to be ΩΛ = 0.865 ± 0.119 in non-flat Lambda cold dark matter (cosmological constant) models, and its equation of state to be $$w=-1.13_{-0.20}^{+0.17}$$ in flat, constant-w models, respectively 41 per cent and 29 per cent tighter than our previous work, and comparable to the best constraints available from other probes. Combining fgas, CMB, supernova, and baryon acoustic oscillation data, we also constrain models with global curvature and evolving dark energy. For the massive, relaxed clusters employed here, we find the scaling of fgas with mass to be consistent with a constant, with an intrinsic scatter that corresponds to just ∼3 per cent in distance.