The properties of exotic nuclei on the verge of existence play a fundamental part in our understanding of nuclear interactions(1). Exceedingly neutron-rich nuclei become sensitive to new aspects of nuclear forces(2). Calcium, with its doubly magic isotopes Ca-40 and Ca-48, is an ideal test for nuclear shell evolution, from the valley of stability to the limits of existence. With a closed proton shell, the calcium isotopes mark the frontier for calculations with three-nucleon forces from chiral effective field theory(3-6). Whereas predictions for the masses of Ca-51 and Ca-52 have been validated by direct measurements(4), it is an open question as to how nuclear masses evolve for heavier calcium isotopes. Here we report the mass determination of the exotic calcium isotopes Ca-53 and Ca-54, using the multi-reflection time-of-flight mass spectrometer(7) of ISOLTRAP at CERN. The measured masses unambiguously establish a prominent shell closure at neutron number N = 32, in excellent agreement with our theoretical calculations. These results increase our understanding of neutron-rich matter and pin down the subtle components of nuclear forces that are at the forefront of theoretical developments constrained by quantum chromodynamics(8).