The displacements of a polystyrene microsphere trapped by an optical tweezers (OT) can be used as a force transducer for mechanical measurements in life sciences such as the measurement of forces of living microorganisms or the viscosity of local fluids. The technique we used allowed us to measure forces on the 200 femto Newtons to 4 pico Newtons range of the protozoa Leishmania amazonensis, responsible for a serious tropical disease. These observations can be used to understand the infection mechanism and chemotaxis of these parasites. The same technique was used to measure viscosities of few microliters sample with agreement with known samples better than 5%. To calibrate the force as a function of the microsphere displacement we first dragged the microsphere in a fluid at known velcoity for a broad range of different optical and hydrodynamical parameters. The hydrodynamical model took into account the presence of two walls and the force depends on drag velocity, fluid viscosity and walls proximities, while the optical model in the geometric optics regime depends on the particle and fluid refractive indexes and laser power. To measure the high numerical (NA) aperture laser beam power after the objective we used an integration sphere to avoid the systematic errors of usual power meters for high NA beams. After this careful laser power measurement we obtained an almost 45 degrees straight line for the plot of the optical force (calculated by the particle horizontal displacement) versus hydrodynamic force (calculated by the drag velocity) under variation of all the parameters described below. This means that hydrodynamic models can be used to calibrate optical forces, as we have done for the parasite force measurement, or vice-versa, as we did for the viscosity measurements.