Central blood pressure (cBP) is a highly prognostic cardiovascular (CV) risk factor whose accurate, invasive assessment is costly and carries risks to patients. We developed and assessed novel algorithms for estimating cBP from non-invasive aortic haemodynamic data and a peripheral BP measurement. These algorithms were created using three blood flow models: the 2-and-3-element Windkessel (0-D) models and a one-dimensional (1-D) model of the thoracic aorta. We tested new and existing methods for estimating CV parameters (ejection time, outflow BP, arterial resistance, compliance, pulse wave velocity, characteristic impedance) required for the cBP algorithms, using 'virtual' subjects (n=19,646) for which reference CV parameters were known exactly. We then tested the cBP algorithms using 'virtual' subjects (n=4,064), for which reference cBP were available free-of-measurement error, and clinical datasets containing invasive (n=10) and non-invasive (n=171) reference cBP waves across a wide-range of CV conditions. The 1-D algorithm outperformed the 0-D algorithms when the aortic vascular geometry was available, achieving central systolic blood pressure (cSBP) errors ≤2.1±9.7mmHg and root-mean-square-errors (RMSEs) ≤6.4±2.8mmHg against invasive reference cBP waves (n=10). When the aortic geometry was unavailable, the 3-element 0-D algorithm achieved cSBP errors ≤6.0±4.7mmHg and RMSEs ≤5.9±2.4mmHg against non-invasive reference cBP waves (n=171), outperforming the 2-element 0-D algorithm. All CV parameters were estimated with mean percentage errors ≤8.2%, except for the aortic characteristic impedance (≤13.4%), which affected the 3-element 0-D algorithm's performance. The freely-available algorithms developed in this work enable fast and accurate calculation of the cBP wave and CV parameters from ultrasound or magnetic resonance imaging data.