Fractals appear from a various sources and have been observed in nature .One of the substantial characteristics of fractals is that they can be described by a non-integer dimension. The geometry and the mathematics of fractal dimension have contributed useful tools for a variety of scientific speciality. The fractal dimension quantifies its dimension across the curves and trajectories. In recent years, various numerical methods have been developed for quantifying the dimension directly from the observations of the natural system. The purpose of this paper is to quantify dimensions of fractals that arise in nature by two fractal quantifiers to quantify the dimensions i.e. compass dimension and box counting dimension thereby deducing an algorithm of chord length and the number of solution steps used in computing fractacality. Results demonstrate that trajectory’s fractal dimension can be nearly approximated. We expect this paper could make the fractal theory understood absolutely, and could expand fractal application in numerous fields.