Masses of the short-lived radionuclides ³²Ar (T_1/2=98   ms) and ³³Ar (T_1/2=173   ms) have been determined with the Penning trap mass spectrometer ISOLTRAP. Relative uncertainties of 6.0×10-8 (δm=1.8   keV) and 1.4×10-8 (δm=0.44   keV), respectively, have been achieved. At present, these new mass data serve as the most stringent test of the quadratic form of the isobaric-multiplet mass equation. Furthermore, the improved accuracy for the mass of ³²Ar will allow for a better constraint on scalar contributions to the weak interaction. New mass values have also been measured for ⁴⁴Ar and ⁴⁵Ar, and a 20σ deviation for ⁴⁴Ar from the literature value was found and interpreted.