In this work, we modify empirical formula with new free-fitting parameters for the \(\left( { n, 2n} \right)\) nuclear reaction cross sections by using the experimental data (EXFOR) from 14 to15 MeV neutron induced energy. We also provide a new empirical formula for 132 isotopes in the mass number range \(6 \le A \le 209\) . In this novel empirical formula, the portion of the nonelastic cross section has been modified by this formula \({ }({\text{A}}^{\frac{1}{3}} + 1)^{2} *\left( \frac{BE}{A} \right)\) , while the asymmetry factor has been included in exponential term. EMPIRE-3.2.3, ALICE-ASH, and TALYS-1.95 were utilized to calculate the \(\left( { n, 2n} \right)\) cross sections of specific isotopes in the 14.5 MeV energy range. The cross sections produced by the updated formulae showed much less chi square and deviations from the experimental data. The results calculated using computer codes and empirical formulae have been compared to previous empirical formulas and, when utilized to correlate the available experimental data of various nuclei, have been shown to be in excellent agreement.
