Fixed reservoir helium permeation leaks are frequently used to generate known flows for calibration of leak detectors. Determination of the flow from helium permeation leaks becomes difficult in the low flow range (10(-12) mol/s, 2 x 10(-8) std. cc/s 273.15 K, and below) which is of high interest to industrial and government users. It has been shown that the flow of a helium permeation leak varies linearly with the helium concentration within the leak reservoir. This relationship was established over a flow range from 10(-11) to 10(-12) mol/s for a particular variable reservoir leak artifact by measuring the flow generated when the reservoir concentration was varied over a range from 4.6 x 10(-1) to 4 x 10(-2) mol/l. Using this relationship, flows in the 10(-13)-10(-14) mol/s region were calculated from measured helium concentrations in the leak artifact reservoir and then compared with the NIST primary leak standard. The results showed agreement, to within experimental error between the two techniques for generating low flows. This technique of generating known low flows by varying the helium concentration in the reservoirs of previously characterized helium permeation leak artifacts has the potential of significantly extending low flow measurements beyond current capabilities.