Numerous neuroimaging studies have investigated the neural basis of inter-individual differences, but the replicability of brain-phenotype associations remains largely unknown. We used the UK Biobank neuroimaging dataset (N=37,462) to examine associations with six variables related to physical and mental health: age, BMI, intelligence, memory, neuroticism, and alcohol consumption, and assessed the improvement of replicability for brain-phenotype associations with increasing sampling sizes. Correlational analyses showed that age may require only 300 individuals to provide highly replicable associations, but other phenotypes required 2700 (memory) to 4800 (neuroticism) individuals. The required sample size showed a negative power law relation with the estimated effect size. When only comparing the upper and lower quarters, the minimally required sample sizes decreased with 15-75%. Our findings demonstrate that large-scale neuroimaging data are required for replicable brain-phenotype associations, that this can be mitigated by preselection of individuals, and that small-scale studies may have reported false positive findings.