The carbon–carbon bonds in the ground states of C2 and C2H2, at their equilibrium geometries, are compared by analysing the changes in the off‐nucleus magnetic shielding tensor within the space surrounding each of these molecules. A wide range of quantum‐chemical approaches, including full‐valence CASSCF‐GIAO, CCSD(T)‐GIAO and CCSDT‐GIAO, all with the cc‐pVQZ basis set, as well as HF‐GIAO and MP2‐GIAO, with the cc‐pVQZ, cc‐pV5Z and cc‐pV6Z basis sets, show that the surroundings of the carbon–carbon bond in C2 are more shielded than those of the carbon–carbon bond in C2H2. The additional shielding of the carbon–carbon bond in C2 is found to be due to a larger paramagnetic contribution to the component of the shielding tensor which is perpendicular to the molecular axis. The analysis of the off‐nucleus shielding data indicates that the carbon–carbon bond in C2 is “bulkier” and, therefore, of a higher multiplicity, but weaker than the corresponding bond in C2H2. According to the results of the shielding calculations, the carbon nuclei in C2 should be much more shielded than those in C2H2, with 13C isotropic magnetic shieldings in the ranges of around 224–227 ppm and around 123–125 ppm for C2 and C2H2, respectively.