Though atomic force microscopy (AFM) interrogates biological materials through mechanical interactions, achieving quantitative mechanical information such as modulus and adhesion at high resolution has been a challenging task. A technology for nanometer scale mechanical property mapping, peak force tapping (PFT), was developed to achieve high resolution imaging and quantitative mechanical measurements simultaneously. PFT controls instantaneous interaction force and record force spectroscopy at each pixel to calculate mechanical properties. A feedback loop maintains a constant peak force, a local maximum point in the force spectroscopy, at the level of Pico Newtons throughout the imaging process. Such high precision force controls enable application of ultra-sharp probe to image biological samples in vitro and achieve molecular resolution in protein membranes. More importantly a full suite of mechanical properties, modulus, adhesion, energy dissipation and deformation are mapped concurrent with topographic imaging. To calculate nanomechanical properties reliably cantilever spring constant and tip shape were calibrated systematically. A method to accurately determine cantilever spring constant, capable of wafer scale cantilever calibration, was developed and tested against traceable force methods. With the knowledge of tip shape, derived from morphological dilation method using a reference sample, mechanical properties measured at the nanometer scale was compared with bench mark materials ranging from 0.7 MPa to 70 GPa. The same method was also applied to OmpG membranes, Lambda DNA strings, as well as live cells. The limitation of the measurement accuracy in biology samples will be discussed.