Nanobubble nucleation is a problem that affects efficiency in electrocatalytic reactions, since those bubbles can block the surface of the catalytic sites. In this article, we focus on the nucleation rate of O2 nanobubbles resulting from electrooxidation of H2O2 at Pt disk nanoelectrodes. Bubbles form almost instantaneously when a critical peak current, pinb is applied, but for lower currents, bubble nucleation is a stochastic process in which the nucleation (induction) time, ind, dramatically decreases as the applied current approaches inbp, a consequence of the local supersaturation level ζ, increasing at high currents. Here, by applying different currents below inbp, nanobubbles take some time to nucleate and block the surface of the Pt electrode at which the reaction occurs, providing a means to measure the stochastic tind. We study in detail the different conditions in which nanobubbles appear, concluding that the electrode surface needs to be pre-conditioned for achieving reproducible results. We also measure the activation energy for bubble nucleation, Ea, which varies in the range from 6 to 30 kT, and, assuming a spherical-cap-shaped nanobubble nucleus, we determine the footprint diameter L=8-15 nm, the contact angle to the electrode surfaceθ=135-155 and the number of O2molecules contained in the nucleus (50 to 900 molecules).