Following on from the second release of calibrated photometry from IPHAS, the INT/WFC Photometric Hα Survey of the Northern Galactic Plane, we present incompleteness-corrected stellar density maps in the r and i photometric bands. These have been computed to a range of limiting magnitudes reaching to 20th magnitude in r and 19th in i (Vega system), and with different angular resolutions – the highest resolution available being 1 arcmin2. The maps obtained cover 94 per cent of the 1800 square degree IPHAS footprint, spanning the Galactic latitude range, −5° < b < +5°, north of the celestial equator. The corrections for incompleteness, due to confusion and sensitivity loss at the faint limit, have been deduced by the method of artificial source injection. The presentation of this method is preceded by a discussion of other more approximate methods of determining completeness. Our method takes full account of position-dependent seeing and source ellipticity in the survey data base. The application of the star counts to testing reddened Galactic disc models is previewed by a comparison with predicted counts along three constant-longitude cuts at ℓ ≃ 30°, 90° and 175°: some overprediction of the most heavily reddened ℓ ≃ 30° counts is found, alongside good agreement at ℓ ≃ 90° and 175°.