The far-infrared spectrum of HC3N has been recorded at high resolution between 70 and 500 cm−1 using synchrotron radiation. Four prominent features, i.e., ν7, ν6−ν7, ν4−ν6, and 2ν7 have been identified in the spectrum together with many associated hot bands. In addition, rotational transitions for the interacting v4=v7=1, (v6=2,v7=1), (v5=1,v7=2), and v7=5 vibrationally excited states have been recorded in the millimeter/submillimeter region. The newly assigned transitions, together with those reported previously, form a comprehensive data set including about 17 000 transitions, which involves almost all the vibrational states of HC3N lying below 1300 cm−1 plus some excited states with energies between 2075 and 3550 cm−1. These data have been fitted to an effective Hamiltonian which takes into account rotational and vibrational l-type resonance effects, together with a number of anharmonic interaction terms. On average, all the analysed data are reproduced within the experimental accuracy. About 90 000 rotational and ro-vibrational transition frequencies have been computed on the basis of the spectroscopic constants obtained from the global fit in order to support data interpretation and astronomical searches in the interstellar medium and planetary atmospheres. Part of these data is included in the 2020 release of the HITRAN database.