  We study the probability that the origin is connected to the sphere of radius
r (an arm event) in critical percolation in high dimensions, namely when the
dimension d is large enough or when d>6 and the lattice is sufficiently spread
out. We prove that this probability decays like 1/r^2. Furthermore, we show
that the probability of having k disjoint arms to distance r emanating from the
vicinity of the origin is 1/r^2k.
