Heterogeneous catalysis is an enabling technology that utilises transition metal nanoparticles (NPs) supported on oxides to promote chemical reactions. Structural mismatch at the NP-support interface generates lattice strain that could affect catalytic properties. However, detailed knowledge about strain in supported NPs remains elusive. We experimentally measure the strain at interfaces, surfaces and defects in Pt NPs supported on alumina and ceria with atomic resolution using high-precision scanning transmission electron microscopy. The largest strains are observed at the interfaces and are predominantly compressive. Atomic models of Pt NPs with experimentally measured strain distributions are used for first-principles kinetic Monte Carlo simulations of the CO oxidation reaction. The presence of only a fraction of strained surface atoms is found to affect the turnover frequency. These results provide a quantitative understanding of the relationship between strain and catalytic function and demonstrate that strain engineering can potentially be used for catalyst design.