High blood pressure (BP) is a major cardiovascular risk factor that is treatable, yet hypertensionawareness and control rates are low. Ubiquitous BP monitoring technology could improve hypertensionmanagement, but existing devices require an inflatable cuff and are not compatible withsuch anytime, anywhere measurement of BP. Oscillometry is the blood pressure (BP) measurementprinciple of most automatic cuff devices. We extended the oscillometric principle, which is usedby most automatic cuff devices, to develop a couple of instruments to measure cuff-less BP usinga smartphone-based device and standalone iPhone application. As the user presses her/his fingeragainst the smartphone, the external pressure of the underlying artery is steadily increased while thephone measures the applied pressure and resulting variable amplitude blood volume oscillations.A smartphone application provides visual feedback to guide the amount of pressure applied overtime via the finger pressing and computes systolic and diastolic BP from the measurements.We prospectively tested the smartphone-based device for real-time BP monitoring in humansubjects to evaluate usability (n = 30) and accuracy against a standard automatic cuff-based device(n = 32). We likewise tested a finger cuff device, which uses the volume-clamp method of BPdetection. About 90% of the users learned the finger actuation required by the smartphone-baseddevice after one or two practice trials. The device yielded bias and precision errors of 3.3 and 8.8mmHg for systolic BP and [Special character(s) omitted]5:6 and 7:7 mmHg for diastolic BP over a 40 to 50 mmHg range of BP.These errors were comparable to the finger cuff device. Cuff-less and calibration-free monitoringof systolic and diastolic BP may be feasible via a smartphone. In addition, we tested the iPhoneapplication. The application yielded bias and precision errors of -4.0 and 11.4 mmHg for systolicBP and -9.4 and 9.7 mmHg for diastolic BP (n = 18). These errors were near the finger cuff deviceerrors. This proof-of-concept study surprisingly indicates that cuff-less and calibration-free BPmonitoring may be feasible with many existing and forthcoming smartphones.These devices use empirical algorithms, already descried in the literature, to estimate bloodpressure. Hence, the next objective was to establish formulas to explain three popular empiricalalgorithms- the maximum amplitude, derivative, and fixed ratio algorithms. A mathematicalmodel of the oscillogram was developed and analyzed to derive parametric formulas for explainingeach algorithm. Exemplary parameter values were obtained by fitting the model to measuredoscillograms. The model and formulas were validated by showing that their predictions correspondto measurements. The formula for the maximum amplitude algorithm indicates that it yields aweighted average of systolic and diastolic BP (0.45 and 0.55 weighting) instead of commonlyassumed mean BP. The formulas for the derivative algorithm indicate that it can accurately estimatesystolic and diastolic BP (1.5 mmHg error), if oscillogram measurement noise can be obviated.The formulas for the fixed ratio algorithm indicate that it can yield inaccurate BP estimates, becausethe ratios change substantially (over a 0.5-0.6 range) with arterial compliance and pulse pressureand error in the assumed ratio translates to BP error via large amplification (40). The establishedformulas allow for easy and complete interpretation of perhaps the three most popular oscillometricBP estimation algorithms in the literature while providing new insights. The model and formulasmay also be of some value towards improving the accuracy of automatic cuff BP measurementdevices.