In this paper, the nonlinear relationship between flowrate and the output pulse of the Roots flowmeter is obtained by analyzing the flowmeter discharge which varies with the angular displacement The errors caused by the nonlinear effect are also estimated. The mathematical models proposed by authors is applicable in calibrating Roots flowmeters efficiently with a compact prover. In addition, it is meaningful for improving the accuracy of the flowmeter's readings on the basis of the results obtained.