The present paper investigates the influence of the specimen size of EN-AW6082 wrought aluminium alloy subjected to very high cycle fatigue (VHCF) tests. The hourglass specimens were tested under fully reversed loading condition, up to 10^9 cycles, by means of the ultrasonic fatigue testing machine developed by Italsigma® (Italy). Three specimens groups were considered, with a diameter in the middle cross-section ranging from 3 mm up to 12 mm. The stress field in the specimens was determined numerically and by strain gauge measurements in correspondence of the cross-section surface. The dispersion of experimental results has been accounted for, and data are reported in P-S-N diagrams. The decrease in fatigue resistance with increasing specimen size is evident. Theoretical explanation for the observed specimen-size effect is provided, based on Fractal Geometry concepts, allowing to obtain scale independent P-S*-N curves. The fatigue life expectation in the VHCF regime of the EN-AW6082 aluminium alloy full-scale components is rather overestimated if it is assessed only from standard small specimens of 3 mm in diameter. Experimental tests carried out on larger specimen, and a proper extrapolation, are required to assure safe structural design.