This paper proposes a novel method to noninvasively measure the peak systolic pressure difference (PSPD) across coarctation of the aorta for diagnosing the severity of coarctation. Traditional non-invasive estimates of pressure drop from the ultrasound can underestimate the severity and invasive measurements by cardiac catheterization can carry risks for patients. To address the issues, we employ computational fluid dynamics (CFD) computation to accurately predict the PSPD across a coarctation based on cardiac magnetic resonance (CMR) imaging data and cuff pressure measurements from one arm. The boundary conditions of a patient-specific aorta model are specified at the inlet of the ascending aorta by using the time-dependent blood velocity, and the outlets of descending aorta and supra aortic branches by using a 3-element Windkessel model. To estimate the parameters of the Windkessel model, steady flow simulations were performed using the time-averaged flow rates in the ascending aorta, descending aorta, and two of the three supra aortic branches. The mean cuff pressure from one arm was specified at the outlet of one of the supra aortic branches. The CFD predicted PSPDs of 5 patients (n=5) were compared with the invasively measured pressure drops obtained by catheterization. The PSPDs were accurately predicted (mean µ=0.3mmHg, standard deviation σ =4.3mmHg) in coarctation of the aorta using completely non-invasive flow and cuff pressure data. The results of our study indicate that the proposed method could potentially replace invasive measurements for estimating the severity of coarctations.Clinical relevance-Peak systolic pressure drop is an indicator of the severity of coarctation of the aorta. It can be predicted without any additional risks to patients using non-invasive cuff pressure and flow data from CMR.