The fundamental period is an essential parameter in the force-based design of buildings as it defines the spectral acceleration and thus the base shear force to which the building should be designed. The fundamental period can be computed based on modeling or utilizing simplified empirical relationships defined in seismic design codes. Previous studies show that the simplified equations should be region-specific and should represent the general design and the construction characteristics of the region. In this study, ambient vibration measurements were carried out on 24 newly constructed, mid-rise reinforced concrete (RC) buildings in Eskisehir, Turkey. The relationships between the fundamental periods and the building heights were examined. Through regression analysis, a simple equation was derived to estimate the elastic fundamental vibration period of mid-rise RC buildings with respect to building height. The proposed relationship was compared to the equation defined in the new Turkey Building Earthquake Code (TBEC-2018) and with the other simplified equations in different design codes and the related literature. The results showed that the fundamental period estimates of the TBEC-2018 equation are much longer than the fundamental periods of the measured buildings in this study. This overestimation may lead to unconservative base shear forces. Therefore, the proposed equation can be used in the force-based design of mid-rise RC frame buildings for conservative estimates of the fundamental period. The contribution of infill walls to the lateral stiffness of the buildings was also investigated, and some preliminary suggestions are made for the related parts in TBEC-2018.