Banding is a type of quantisation artefact that appears when a low-texture region of an image is coded with insufficient bitdepth. Banding artefacts are well-studied for standard dynamic range (SDR), but are not well-understood for high dynamic range (HDR). To address this issue, we conducted a psychophysical experiment to characterise how well human observers see banding artefacts across a wide range of luminances (0.1 cd/m²–10,000 cd/m²). The stimuli were gradients modulated along three colour directions: black-white, red-green, and yellow-violet. The visibility threshold for banding artefacts was the highest at 0.1 cd/m², decreased with increasing luminance up to 100 cd/m², then remained at the same level up to 10,000 cd/m². We used the results to develop and validate a model of banding artefact detection. The model relies on the contrast sensitivity function (CSF) of the visual system, and hence, predicts the visibility of banding artefacts in a perceptually accurate way.