We have shown that a polynomial equation, F(P)=AP³+BP²+CP+D, can accurately determine the presence of inspiratory flow limitation (IFL). This equation requires the invasive measurement of supraglottic pressure. We hypothesized that a modification of the equation that substitutes time for pressure would be accurate for the detection of IFL and allow for the noninvasive measurement of upper airway resistance. The modified equation is F(t) = At³+Bt²+Ct+D, where F=flow, t=time from the onset of inspiration. To test our hypotheses, data analysis was performed as follows on 440 randomly chosen breaths from 18 subjects. First, we performed linear regression and determined that there is a linear relationship between pressure and time in the upper airway (R² 0.96±0.05, slope 0.96±0.06), indicating that time can be a surrogate for pressure. Second, we performed curve fitting and found that polynomial equation accurately predicts the relationship between flow and time in the upper airway (R² 0.93±0.12, error fit 0.02±0.08). Third, we performed a sensitivity/specificity analysis comparing the mathematical determination of IFL to manual determination using a pressure-flow loop. Mathematical determination had both high sensitivity (96%) and specificity (99%). Fourth, we calculated the upper airway resistance (cRUA) using the polynomial equation and compared the measurement to the manually determined upper airway resistance (mRUA; also from a pressure-flow loop) using Bland-Altman analysis. Mean difference between cRUA and mRUA was 0.0 cmH₂O/l/s (95%CI -0.2, 0.2) with upper and lower limits of agreement of 2.8 cmH₂O/l/s and -2.8 cmH₂O/l/s. We conclude that a polynomial equation can be used to model the flow-time relationship, allowing for the objective and accurate determination of upper airway resistance and the presence of IFL.