We have used the Australia Telescope Compact Array (ATCA) and the Swedish–ESO Submillimetre Telescope (SEST) to map the large‐scale atomic and molecular gas in the nearby (4 Mpc) Circinus galaxy. The ATCA H i mosaic of Circinus exhibits the warps in position angle and inclination revealed in the single‐pointing image of Jones et al., both of which appear to settle beyond the inner 30 kpc which was previously imaged. The molecular gas has been mapped in both the CO J= 1 → 0 and J= 2 → 1 transitions down to a column density of (3σ), where we derive a total molecular gas mass of . Within a radius of 3 kpc, i.e. where CO was clearly detected, the molecular fraction climbs steeply from ≈ 0.7 to unity (where , cf. NH i= 1021 cm−2) with proximity to the nucleus. Our H i mosaic gives an atomic gas mass of MH i≈ 6 × 109 M⊙, which is 70 per cent of the fully mapped single dish value. Combining the atomic and molecular gas masses gives a total gas mass of , cf. the total dynamical mass of ≈ 3 × 1011 M⊙ within the inner 50 kpc of our mosaiced image. The total neutral gas mass to dynamical mass ratio is therefore 3 per cent, consistent with the SAS3 (Third Small Astronomy Satellite) classification of Circinus. The high (molecular) gas mass fraction of per cent found by Curran et al., only occurs close to the central ≈ 0.5 kpc and falls to ≲10 per cent within and outwith this region, allaying previous concerns regarding the validity of applying the Galactic conversion ratio to Circinus. The rotation curve, as traced by both the H i and CO, exhibits a steep dip at ≈ 1 kpc, the edge of the atomic/molecular ring, within which the starburst is occurring. We find the atomic and molecular gases to trace different kinematical features and believe that the fastest part (≳130 km s−1) of the subkpc ring consists overwhelmingly of molecular gas. Beyond the inner kpc, the velocity climbs to settle into a solid body rotation of ≈ 150 km s−1 at ≳10 kpc. Most of the starlight emanates from within this radius and so much of the dynamical mass, which remains climbing to the limit of our data (≳50 kpc), must be due to the dark matter halo.