Fast scanning calorimetry is an attractive tool to study kinetics and thermodynamics of materials created or used far from thermodynamic equilibrium. In the first part of this paper we describe a differential fast scanning nano-calorimeter utilizing a new power compensation scheme. The device is suitable for calorimetric experiments at controlled cooling and heating rates between 1 and 100,000 K/s. This part of the paper focuses on determination of specific heat capacity out of the measured data. Assuming time independent heat losses for sample and reference sensors at heating and cooling makes possible a heat capacity analysis based on symmetry arguments. The described procedure is not limited to chip-based fast scanning devices but can be applied to common DSC too. Due to the differential scheme and power compensation heat capacity of polymer samples with sample mass of a few 10 ng is available. Reproducibility of heat capacity is in the order of +/- 2% at optimum scanning rates. Uncertainty of specific heat capacity strongly depends on sample mass determination and is in the order of +/- 10%. Adding a small particle of a temperature calibration standard, e.g. indium or tin, on top of the polymer sample reduces uncertainty of temperature to about +/- 4 K. (C) 2010 Elsevier B.V. All rights reserved.