Deciding whether to forgo a good choice in favour of exploring a potentially more rewarding alternative is one of the most challenging arbitrations both in human reasoning and in artificial intelligence. Humans show substantial variability in their exploration, and theoretical but only limited empirical work has suggested that excessive exploration is a critical mechanism underlying the psychiatric dimension of impulsivity. We put these theories to test using a large online sample (N=580 healthy adults), dimensional analyses, and computational modelling in a pre-registered study. Capitalising on recent advances in disentangling distinct human exploration strategies, we demonstrate that impulsivity is associated with a specific form of exploration, value-free random exploration, a computationally light exploration heuristic. Our results not only demonstrate this specific association with impulsivity, but also explore links between exploration and other psychiatric dimensions.