This paper presents a design and construction of a 16-point FFT calculator based on FPGA technology. Specifically, the data is complex numbers in which the real and imaginary parts are represented as fixed-point real numbers. Moreover, a fixed-point real number is defined by 16 bits with the high-significant bit being the 2's complement bit, the next 9 bits being the integer part, and the last 6 bits being the fractional part. By means of simulations and FPGA board-based experimental results, we show the advantage of the proposed design compared to the existing ones. The operating frequency of the system is 149,867 MHz giving 4,683,343 FFT calculations of 16-points per second with low error (only about 0.3). This design of FFT calculator could be extensible to perform multi-point transformations since it is designed in a pipeline architecture with modules that are easily resizable and can be embedded in systems that require the 16-point FFT calculator.