We present electrical characterization including throughout noise investigations of a three-dimensional nano Superconducting QUantum Interference Device (nanoSQUIDs) fabricated with Focused Ion Beam sculpturing technique. The use of superconductor- isolator-superconductor (SIS) Nb/Al-AlOx/Nb Josephson tunnel junctions together with small SQUID loop dimensions permit a high modulation depth of the SQUID’s critical current and thus lead to very low intrinsic flux noise of the device. At 4.2 K two-stage noise measurements with a SQUID as a low noise preamplifier results in a white flux noise of 55 n0/Hz1/2, equivalent to an energy resolution of 1.5 h, with h being Planck’s constant. Simulation of spin sensitivities result in about 1 µB/Hz1/2 for an electron spin positioned directly above the SQUID ring.