Rotational spectroscopy has been used for decades for virtually unambiguous identification of gas phase molecular species, but it has rarely been used for the quantitative analysis of molecular concentrations. Challenges have included the nontrivial reconstruction of integrated line strengths from modulated spectra, the correlation of pressure-dependent line shape and strength with partial pressure, and the multiple standing wave interferences and modulation-induced line shape asymmetries that sensitively depend on source-chamber-detector alignment. Here, we introduce a quantitative analysis methodology that overcomes these challenges, reproducibly and accurately recovering gas molecule concentrations using a calibration procedure with a reference gas and a conversion based on calculated line strengths. The technique uses frequency-modulated rotational spectroscopy and recovers the integrated line strength from a Voigt line shape that spans the Doppler- and pressure-broadened regimes. Gas concentrations were accurately quantified to within the experimental error over more than three orders of magnitude, as confirmed by the cross calibration between CO and N2O and by the accurate recovery of the natural abundances of four N2O isotopologues. With this methodology, concentrations of hundreds of molecular species may be quantitatively measured down to the femtomolar regime using only a single calibration curve and the readily available libraries of calculated integrated line strengths, demonstrating the power of this technique for the quantitative gas-phase detection, identification, and quantification.