Abstract Pulse profile modelling (PPM) is a comprehensive relativistic ray-tracing technique employed to determine the properties of neutron stars. In this study, we apply this technique to the Type I X-ray burster and accretion-powered millisecond pulsar J, extracting its fundamental properties using PPM of its thermonuclear burst oscillations. Using data from its 2003 outburst, and a single uniform temperature hot spot model, we infer J to be located at a distance of $7.2^{+0.3}_{-0.4}$ kpc, with a mass of $1.21^{+0.05}_{-0.05}$ M⊙ and an equatorial radius of $7.0^{+0.4}_{-0.4}$ km. Our results also offer insight into the time evolution of the hot spot but point to some potential shortcomings of the single uniform temperature hot spot model. We explore the implications of this result, including what we can learn about thermonuclear burst oscillation mechanisms and the importance of modelling the accretion contribution to the emission during the burst.