We present Atacama Large Millimeter/submillimeter Array observations of 99.02 GHz free–free and H40α emission from the centre of the nearby starburst galaxy NGC 253. We calculate electron temperatures of 3700–4500 K for the photoionized gas, which agrees with previous measurements. We measure a photoionizing photon production rate of (3.2 ± 0.2) × 1053 s−1 and a star formation rate of 1.73 ± 0.12 M⊙ yr−1 within the central 20 × 10 arcsec, which fall within the broad range of measurements from previous millimetre and radio observations but which are better constrained. We also demonstrate that the dust opacities are ∼3 dex higher than inferred from previous near-infrared data, which illustrates the benefits of using millimetre star formation tracers in very dusty sources.