We present an open source kinematic fitting routine designed for low-energy nuclear physics applications. Although kinematic fitting is commonly used in high-energy particle physics, it is rarely used in low-energy nuclear physics, despite its effectiveness. A FORTRAN and ROOT C++ version of the FUNKI_FIT kinematic fitting code have been developed and published open access. The FUNKI_FIT code is universal in the sense that the constraint equations can be easily modified to suit different experimental set-ups and reactions. Two case studies for the use of this code, utilising experimental and Monte-Carlo data, are presented: (1) charged-particle spectroscopy using silicon-strip detectors; (2) charged-particle spectroscopy using active target detectors. The kinematic fitting routine provides an improvement in resolution in both cases, demonstrating, for the first time, the applicability of kinematic fitting across a range of nuclear physics applications. The ROOT macro has been developed in order to easily apply this technique in standard data analysis routines used by the nuclear physics community.