Geometrical and material — i.e., external and internal — scaling symmetries are exploited to obtain approximated analytical expressions for the mode effective index, group index, and chromatic dispersion of a scaled fiber. Our results include material refractive index scaling that changes the numerical aperture. First, the analytical expressions are successfully tested with a conventional step index fiber in a broadband range of wavelengths, from 1 to 2 μm. Then, we establish a procedure to adapt the analytical expressions to photonic crystal fibers (PCFs) and illustrate its application in a triangular PCF with circular holes. These adapted analytical expressions show good agreement with a rigorous numerical solution of the fundamental fiber mode. Finally, we demonstrate how powerful these expressions are for the design of PCFs. In particular, we illustrate our approach designing, in four iterations or less, PCFs with flattened dispersion profile over 300 nm or high dispersion slope over 40 nm, with different chromatic dispersion values.