The techniques of neutron interferometry and neutron diffraction were used to determine the coherent and incoherent neutron scattering lengths of ¹³C. From a neutron interferometry measurement of the optical path difference in liquid samples, ¹³CS₂ versus ^natCS₂, we obtain a bound coherent scattering length of b_coh,13C = 6.542 ± 0.003 fm, which differs appreciably from the standard tabulated value of 6.19 ± 0.09 fm. The resulting contrast of only 0.106(3) fm with respect to b_coh,natC = 6.6484 ± 0.0013 fm has consequences for neutron diffraction experiments involving ¹³C isotopic substitution. Combining our result for b_coh,13C with precise neutron diffraction measurements of the self-scattering intensities of liquid samples, ¹³CS₂ versus ^natCS₂, and ¹³CO₂ versus ¹²CO₂, we deduce a bound incoherent scattering length of b_incoh,13C = −0.42 ± 0.24 fm that is consistent with the standard tabulated value of −0.52 ± 0.09 fm. The results presented here have required accurate measurements of small effects, for which particular attention has been given to the data analysis.