  In this paper, we investigate the nonrelativistic limit of normalized
solutions to a nonlinear Dirac equation as given below: \begin{equation*}
  \begin{cases} &-i c\sum\limits_{k=1}^3\alpha_k\partial_k u +mc^2 \beta {u}-
\Gamma * (K |{u}|^\kappa) K|{u}|^{\kappa-2}{u}- P |{u}|^{s-2}{u}=\omega {u}, \\
&\displaystyle\int_{\mathbb{R}^3}\vert u \vert^2 dx =1.
  \end{cases} \end{equation*} Here, $c>0$ represents the speed of light, $m >
0$ is the mass of the Dirac particle, $\omega\in\mathbb{R}$ emerges as an
indeterminate Lagrange multiplier, $\Gamma$, $K$, $P$ are real-valued function
defined on $\mathbb{R}^3$, also known as potential functions. Our research
first confirms the presence of normalized solutions to the Dirac equation under
high-speed light conditions. We then illustrate that these solutions progress
to become the ground states of a system of nonlinear Schr\"odinger equations
with a normalized constraint, exhibiting uniform boundedness and exponential
decay irrespective of the light speed. Our results form the first discussion on
nonrelativistic limit of normalized solutions to nonlinear Dirac equations.
This not only aids in the study of normalized solutions of the nonlinear
Schr\"odinger equations, but also physically explains that the normalized
ground states of high-speed particles and low-speed motion particles are
consistent.
