Abstract The initial period of a pulsar is an important factor in our understanding of the formation of neutron stars and of the nature of the equation of state of neutron star matter. Up to now this quantity can only be obtained for a few pulsars for which accurate age and braking index are known. Based on the theory of the off-center dipole emission, in which pulsars obtain their high velocities depending on the initial periods, we calculate the initial period using the proper motion data. Because the orbital velocity of the progenitor and asymmetric kick in the supernova explosion may also contribute to the observed velocity of the pulsar, the derived values of initial periods are lower limits. For normal pulsars, the initial periods are in the range of 0.6 ∼ 2.6 ms. For the millisecond pulsars, the initial periods are comparable to their current periods, and the ratio between the initial period and the current period increases with the decrease of the current period. For PSR B1937+21 with the shortest period of 1.56 ms, the ratio is 0.77.

Keywords pulsars --- stars: neutron

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