Context. Rapid rotation is a common feature for massive stars, with important consequences on their physical structure, flux distribution and evolution. Fast-rotating stars are flattened and show gravity darkening (non-uniform surface intensity distribution). Another important and less studied impact of fast-rotation in early-type stars is its influence on the surface brightness colour relation (hereafter SBCR), which could be used to derive the distance of eclipsing binaries. <BR /> Aims: The purpose of this paper is to determine the flattening of the fast-rotating B-type star δ Per using visible long-baseline interferometry. A second goal is to evaluate the impact of rotation and gravity darkening on the V – K colour and surface brightness of the star. <BR /> Methods: The B-type star δ Per was observed with the VEGA/CHARA interferometer, which can measure spatial resolutions down to 0.3 mas and spectral resolving power of 5000 in the visible. We first used a toy model to derive the position angle of the rotation axis of the star in the plane of the sky. Then we used a code of stellar rotation, CHARRON, in order to derive the physical parameters of the star. Finally, by considering two cases, a static reference star and our best model of δ Per, we can quantify the impact of fast rotation on the surface brightness colour relation (SBCR). <BR /> Results: We find a position angle of 23 ± 6 degrees. The polar axis angular diameter of δ Per is θ<SUB>p</SUB> = 0.544 ± 0.007 mas, and the derived flatness is r = 1.121 ± 0.013. We derive an inclination angle for the star of I = 85<SUP>+ 5</SUP><SUB>-20</SUB> degrees and a projected rotation velocity Vsini = 175<SUP>+ 8</SUP><SUB>-11</SUB> km s<SUP>-1</SUP> (or 57% of the critical velocity). We find also that the rotation and inclination angle of δ Per keeps the V – K colour unchanged while it decreasing its surface-brightness by about 0.05 mag. <BR /> Conclusions: Correcting the impact of rotation on the SBCR of early-type stars appears feasible using visible interferometry and dedicated models.
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