The health effects of cosmic radiation on astronauts need to be precisely quantified and controlled. This task is important not only in perspective of the increasing human presence at the International Space Station (ISS), but also for the preparation of safe human missions beyond low earth orbit. From a radiation protection point of view, the baseline quantity for radiation risk assessment in space is the effective dose equivalent. The present work reports the first successful attempt of the experimental determination of the effective dose equivalent in space, both for extra-vehicular activity (EVA) and intra-vehicular activity (IVA). This was achieved using the anthropomorphic torso phantom RANDO® equipped with more than 6,000 passive thermoluminescent detectors and plastic nuclear track detectors, which have been exposed to cosmic radiation inside the European Space Agency MATROSHKA facility both outside and inside the ISS. In order to calculate the effective dose equivalent, a numerical model of the RANDO® phantom, based on computer tomography scans of the actual phantom, was developed. It was found that the effective dose equivalent rate during an EVA approaches 700 μSv/d, while during an IVA about 20 % lower values were observed. It is shown that the individual dose based on a personal dosimeter reading for an astronaut during IVA results in an overestimate of the effective dose equivalent of about 15 %, whereas under an EVA conditions the overestimate is more than 200 %. A personal dosemeter can therefore deliver quite good exposure records during IVA, but may overestimate the effective dose equivalent received during an EVA considerably.