The magnetic measurements on single cobalt and iron nanoclusters containing almost 1000 atoms are presented. Particles are directly buried within the superconducting film of a micro-SQUID (superconducting quantum interference device) which leads to the required sensitivity. The angular dependence of the switching field in three dimensions turns out to be in good agreement with a uniform rotation of cluster magnetization. The Stoner and Wohlfarth model yields therefore an estimation of magnetic anisotropy in a single cluster. In particular, uniaxial, biaxial, and cubic contributions can be separated. Results are interpreted on the basis of a simple atomic model in which clusters are assimilated to ``giant spins.'' We present an extension of the N\'eel model to clusters in order to estimate surface anisotropy. In the case of cobalt, this last contribution dominates and numerical simulations allow us to get the morphology of the investigated clusters.