Dust extinction is one of the fundamental measurements of dust grain sizes, compositions, and shapes. Most of the wavelength-dependent variations seen in Milky Way extinction are strongly correlated with the single parameter R (V)= A (V)/E (B− V). Existing R (V)-dependent extinction relationships use a mixture of spectroscopic and photometry observations, and hence do not fully capture all the important dust features or continuum variations. Using four existing samples of spectroscopically measured dust extinction curves, we consistently measure the R (V)-dependent extinction relationship spectroscopically from the far-ultraviolet (FUV) to mid-infrared for the first time. Linear fits of A (λ)/A (V) dependent on R (V) are done using a method that fully accounts for their significant and correlated uncertainties. These linear parameters are fit with analytic wavelength-dependent functions to determine the smooth R (V)(2.3–5.6) and wavelength (912 �–32 μm) dependent extinction relationship. This relationship shows that the FUV rise, 2175 � bump, and the three broad optical features are dependent on R (V), but the 10 and 20 μm features are not. Existing literature relationships show significant deviations compared to this relationship especially in the FUV and infrared (IR). Extinction curves that clearly deviate from this relationship illustrate that this relationship only describes the average behavior versus R (V). We find tentative evidence that the relationship may not be linear with R (V)− 1 especially in the ultraviolet (UV). For the first time, this relationship provides measurements of dust extinction that spectroscopically resolve the continuum and features in the UV, optical, and IR as a function of R (V), enabling detailed studies of dust grain properties and full spectroscopic accounting for the effects of dust extinction on astrophysical objects.