Long cylinders, such as optical fibers, are some of the most widely used photonic devices. The radius and refractive index of these fibers are therefore fundamentally important parameters in determining their performance. We have developed a method to determine the absolute radius, refractive index, and chromatic dispersion of a long cylinder using only the resonance wavelengths of the whispering gallery modes around its circumference for two different polarizations. Since this method only requires the measurement of resonance wavelengths, it is non-destructive and it can be performed using standard equipment. As a proof-of-concept, we demonstrate the method on a 125µm optical fiber and an 80µm borosilicate capillary fiber with thick walls, obtaining values for the diameter and the refractive index with an accuracy of 2 nm and 2 × 10-5, respectively.