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Neutron elastic scattering cross sections on natural carbon serve as a reference standard in the incident energy range 10 eV to 1.8 MeV. The 2017 standards evaluation [1, 2] is 0.5 to 2.0% higher in that energy range than the 2006 standards evaluation [3]. In addition the ENDF/B-VIII.0 release split the natural carbon cross sections into the isotopes¹²C,¹³C, and¹⁴C for the first time. These details call for the re-measurement of the¹³C cross sections in sensitive regions. Ten elastic scattering angular distributions were recently measured for incident neutron energies between 0.5 and 3.25 MeV at the University of Kentucky Accelerator Laboratory (www.pa.uky.edu/accelerator/) using nanosecond pulsed beams and time-of-flight techniques. An overview of neutron production and detection, the new digital data acquisition system, and data analysis will be presented. Results are compared with data from previous measurements and database evaluations.