Abstract We present high-precision, model-independent, mass and radius measurements for 16 white dwarfs in detached eclipsing binaries and combine these with previously published data to test the theoretical white dwarf mass–radius relationship. We reach a mean precision of 2.4 per cent in mass and 2.7 per cent in radius, with our best measurements reaching a precision of 0.3 per cent in mass and 0.5 per cent in radius. We find excellent agreement between the measured and predicted radii across a wide range of masses and temperatures. We also find the radii of all white dwarfs with masses less than 0.48 M⊙ to be fully consistent with helium core models, but they are on average 9 per cent larger than those of carbon–oxygen core models. In contrast, white dwarfs with masses larger than 0.52 M⊙ all have radii consistent with carbon–oxygen core models. Moreover, we find that all but one of the white dwarfs in our sample have radii consistent with possessing thick surface hydrogen envelopes (10−5 ≥ M H/M WD ≥ 10−4), implying that the surface hydrogen layers of these white dwarfs are not obviously affected by common envelope evolution.