A novel method for graphically and mathematically representing the dispersion characteristics of electromagnetic dielectric structures is presented. The method has been used to develop closed-form formulas to find the longitudinal propagation constant and useful frequency range for a number of popular rectangular dielectric waveguide types. These formulas are presented in terms of their material dependency and are guide size and operating frequency independent. Their form is so trivial that these characteristics can now be found in just a few seconds using a basic calculator, yet still with second order accuracy. In addition, improvements have been made to a number of well-known formulas normally associated with periodic grating leaky-wave antennas. These improvements allow the width of the metal strip grating to be taken into consideration to derive the correct main beam angle, array factor pattern and grating limits. Previously, the grating width was neglected by the formulas and the resulting error was unacceptably high.