A fractional concentration of clinically-relevant DNA in a mixture of DNA from a biological sample is determined based on amounts of DNA fragments at multiple sizes. For example, the fractional concentration of fetal DNA in maternal plasma or tumor DNA in a patient's plasma can be determined. The size of DNA fragments in a sample is shown to be correlated with a proportion of fetal DNA and a proportion of tumor DNA, respectively. Calibration data points (e.g., as a calibration function) indicate a correspondence between values of a size parameter and the fractional concentration of the clinically-relevant DNA. For a given sample, a first value of a size parameter can be determined from the sizes of DNA fragments in a sample. A comparison of the first value to the calibration data points can provide the estimate of the fractional concentration of the clinically-relevant DNA.