We show that the bound from the electroweak data on the size of extra dimensions accessible to all the standard model fields is rather loose. These "universal" extra dimensions could have a compactification scale as low as 300 GeV for one extra dimension. This is because the Kaluza-Klein number is conserved and thus the contributions to the electroweak observables arise only from loops. The main constraint comes from weak-isospin violation effects. We also compute the contributions to the S parameter and the $Zb\bar{b}$ vertex. The direct bound on the compactification scale is set by CDF and D0 in the few hundred GeV range, and the Run II of the Tevatron will either discover extra dimensions or else it could significantly raise the bound on the compactification scale. In the case of two universal extra dimensions, the current lower bound on the compactification scale depends logarithmically on the ultra-violet cutoff of the higher dimensional theory, but can be estimated to lie between 400 and 800 GeV. With three or more extra dimensions, the cutoff dependence may be too strong to allow an estimate.

22 pages, Latex, 1 eps figure. Published version; minor correction in the Kaluza-Klein decomposition