The recent fast growth of a population of millisecond pulsars with precisely measured mass provides an excellent opportunity to characterize these compact stars at an unprecedented level. This is because the stellar parameter values can be accurately computed for known mass and spin rate and an assumed equation of state (EoS) model. For each of the 16 such pulsars and for a set of EoS models from nucleonic, hyperonic, strange quark matter and hybrid classes, we numerically compute fast spinning stable stellar parameter values considering the full effect of general relativity. This first detailed catalogue of the computed parameter values of observed millisecond pulsars provides a testbed to probe the physics of compact stars, including their formation, evolution and EoS. We estimate uncertainties on these computed values from the uncertainty of the measured mass, which could be useful to quantitatively constrain EoS models. We note that the largest value of the central density $rho_{rm c}$ in our catalogue is $sim 5.8$ times the nuclear saturation density $rho_{rm sat}$, which is much less than the expected maximum value $13 rho_{rm sat}$. We argue that the $rho_{rm c}$-values of at most a small fraction of compact stars could be much larger than $5.8 rho_{rm sat}$. Besides, we find that the constraints on EoS models from accurate radius measurements could be significantly biased for some of our pulsars, if stellar $spinning$ configurations are not used to compute the theoretical radius values.
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