An innovative nanocalorimeter has been developed for measuring specific heats of thin films, multilayers (typical thickness: 1000 Å) and single crystals (mass: 1 &mgr;g) in the temperature range of 1.5–20 K. The addenda of the device are as small as 3 nJ/K at 4 K (0.5 nJ/K at 1.5 K), thus samples with a heat capacity of the order of nJ/K at 4 K can be measured. Heat capacity differences as a function of temperature or an external magnetic field (5 T) were determined with a resolution of&Dgr;C/C≃10−4.This way we have seen heat capacity variations of less than a pJ/K. We present as an example measurements on very smallMn12O12acetate single crystals and a measurement of a thin superconducting Pb layer. In the latter measurement we could evidence via specific heat a finite size effect. ©1997 American Institute of Physics.