We present multi-epoch observations of the radio nebula around the neutron star X-ray binary Circinus X-1 made at 1.4 and 2.5 GHz with the Australia Telescope Compact Array between 2000 October and 2004 September. The nebula can be seen as a result of the interaction between the jet from the system and the interstellar medium and it is likely that we are actually looking toward the central X-ray binary system through the jet-powered radio lobe. The study of the nebula thus offers a unique opportunity to estimate for the first time using calorimetry the energetics of a jet from an object clearly identified as a neutron star. An extensive discussion on the energetics of the complex is presented: a first approach is based on the minimum energy estimation, while a second one employs a self-similar model of the interaction between the jets and the surrounding medium. The results suggest an age for the nebula of ≤105 yr and a corresponding time-averaged jet power ≥1035 erg s−1. During periodic flaring episodes, the instantaneous jet power may reach values of similar magnitude to the X-ray luminosity.