Aortic stenos (AS) is a heart valve disease that commonly affects the elderly. Transcatheter aortic valve implantation is a minimally invasive treatment that allows to replace the function of the diseased native valve with a prosthetic device, relying on catheters for device implantation. According to the current clinical guidelines, the choice of the implanted device is based on preoperative sizing determined by image-based technology. However, this assessment faces inherent limitations that can lead to sub-optimal sizing of the prosthesis; in turn, this can cause major post-operative complications like aortic regurgitation or cardiac electrical signal disruption. By utilizing balloon pressure and volume data, this article proposes an intra-operative method for determining the dimension of the aortic annulus which takes into account its compliance and geometric irregularity. The intra-balloon pressure-volume curves were obtained using an Automated Balloon Inflation Device operating a commercially available valvuloplasty balloon catheter. A sizing algorithm to estimate the dimensions of the annulus was integrated via a validated analytical model and a numerical model for balloon free-inflation. Tests were performed on circular and elliptical idealised aortic phantoms. Experimental results confirm that the pressure-volume data processed with the sizing algorithm can be used to determine the circular annular diameter for all tissue rigidities. The measurement of stiffer elliptical annulus phantoms shows good accuracy and high repeatability. This work represents substantial progress toward improving the selection of TAVI devices by using balloon catheters to improve the sizing of compliant aortic annuli with complex geometry.