Astronomical wide-field imaging of interferometric radio data is computationally expensive, especially for the large data volumes created by modern non-coplanar many-element arrays. We present a new wide-field interferometric imager that uses the w-stacking algorithm and can make use of the w-snapshot algorithm. The performance dependences of CASA's w-projection and our new imager are analysed and analytical functions are derived that describe the required computing cost for both imagers. On data from the Murchison Widefield Array, we find our new method to be an order of magnitude faster than w-projection, as well as being capable of full-sky imaging at full resolution and with correct polarization correction. We predict the computing costs for several other arrays and estimate that our imager is a factor of 2–12 faster, depending on the array configuration. We estimate the computing cost for imaging the low-frequency Square Kilometre Array observations to be 60 PetaFLOPS with current techniques. We find that combining w-stacking with the w-snapshot algorithm does not significantly improve computing requirements over pure w-stacking. The source code of our new imager is publicly released.