To aid in the design of electrooptic devices, a simplified procedure is introduced for determining the principal indices of refraction and the orientations of the index ellipsoid when an electric field is applied. The approach employs the general Jacobi method, and it is applicable to an arbitrary isotropic, uniaxial, or biaxial crystal class with an arbitrary direction of applied field. It includes a straightforward approach for labeling the new principal dielectric axes so as to produce the minimum global rotation of the ellipsoid from the zerofield principal dielectric axes. The necessary calculations can be easily implemented with a pocket calculator and are often found to be more accurate than those obtained with larger computers using standard library math packages. Furthermore, for analyzing device performance, simple analytic expressions for the orientations of the fast and slow polarization axes and the fast and slow indices of refraction are derived for a given arbitrary direction of optical propagation and any arbitrary direction of applied electric field. The calculational procedure is applicable to linear and quadratic electrooptic effects and the photoelastic effect in isotropic, uniaxial, and biaxial crystals. Illustrative examples for GaAs, LiNbO(3), and KDP are presented.