Improved opacities are needed for modelling the atmospheres and evolution of cool carbon-rich stars and extra-solar planets; in particular, contributions made by the astrophysically important propadienediylidene (C3) molecule need, at a minimum, to be determined using a line list which includes all significant transitions in the energy range of interest. We report variational calculations giving ro-vibrational energy levels and corresponding line-strengths for 12C3, 12C13C12C and 12C12C13C. In the 12C3 case we obtain 2 166 503 ro-vibrational state energies ≤20000 cm−1 for the electronic $\tilde{X}{\, }^{1}{\Sigma _{\rm g}}^{+}$ ground-state. Comparison with experiment indicates a maximum error of ±0.03 cm−1 in calculated positions of lines involving an upper state energy ⪅4000 cm−1. For lines with upper state energies ⪆4000 cm−1 to have comparable line-position accuracies, conical intersections would need to be accounted for in an adopted potential energy surface. Line lists and associated opacities are provided in the ExoMol Database (http://www.exomol.com).