Since its introduction in the 1970s, Fluorescence Correlation Spectroscopy (FCS) has become a standard biophysical and bioengineering tool to investigate diffusion processes in living cells complementing other fluorescence microscopy techniques including but not limited to Fluorescence Recovery after Photobleaching (FRAP) and Single Particle Tracking (SPT). For diffusion FCS analysis, an autocorrelation curve of fluorescence fluctuation data is compared with a theoretical autocorrelation function or FCS equation for a diffusion coefficient. Additionally, FCS is now being applied not only to a diffusion process but also to a broad range of biochemical processes including binding kinetics and anomalous diffusion. Since the derivation of FCS equations for many biochemical processes shares many common steps with the diffusion FCS equation, it is important to understand mathematical theory behind the diffusion FCS equation. However, because the derivation of FCS equations requires advanced Fourier Transform and inverse Fourier Transform involving intermediate to advance level mathematical techniques, which most biologists and bioengineers are not familiar with, it is often treated as a black box in the classroom. In this tutorial, we provide a simple and straightforward derivation of FCS equation for free diffusion based on calculus-level mathematics without the knowledge of Fourier transform and inverse Fourier transform, so that FCS equations and its applications are accessible to a broad audience.Since its introduction in the 1970s, Fluorescence Correlation Spectroscopy (FCS) has become a standard biophysical tool to investigate diffusion process in living cells complementing other fluorescence microscopy techniques including but not limited to Fluorescence Recovery after Photobleaching (FRAP) and Single Particle Tracing (SPT). For diffusion FCS analysis, an autocorrelation curve of fluorescence fluctuation data is compared for a diffusion coefficient with a theoretical autocorrelation function or FCS equation, which is derived based on the stationary and ergodic assumptions on Brownian motion. However, due to simplicity of FCS analysis, FCS is now being applied not only to diffusion process but also a broad range of biochemical processes such as binding kinetics and anomalous diffusion process which may not satisfy the stationary and ergodic assumptions of FCS equations. Furthermore, in many applications in biology, variations of FCS equations modified from a diffusion FCS equation are being used treating derivation steps of the FCS equations as a blackbox mainly due to computational complexity involving intermediate to advance level mathematical techniques, which most biologists are not familiar with. So, this study serves as two-folds: (1) Here, we derive a FCS equation for free diffusion without stationary and ergodic assumptions, so that various modifications of FCS equations in the literature can be justified and (2) we provide a simple and straightforward derivation of FCS equation for free diffusion based on calculus level mathematics without the konwledge of Fourier transform and inverse Fourier transform, so that FCS equations and its applications are accessible to a broad audience.