Streams are categorized into perennial and temporal streams based on flow durations. Perennial stream is the basic network, and temporal stream (ephemeral or intermittent) is the expanded network. Connection between perennial stream and runoff generation at the mean annual scale exists since one of the hydrologic functions of perennial stream is to deliver runoff. The partitioning of precipitation into runoff and evaporation at the mean annual scale, on the first order, is represented by the Budyko hypothesis which quantifies the ratio of evaporation to precipitation (E/P) as a function of climate aridity index (Ep/P, ratio of potential evaporation to precipitation). In this paper, it is hypothesized that similarity exists between perennial stream density (Dp) and runoff coefficient (Q/P) as a function of climate aridity index, i.e., DpDp* (EpP) and QP (EpP) where Dp* is a scaling factor and Q is mean annual runoff. To test the hypothesis, perennial stream densities for 185 watersheds in the United States are computed based on the high resolution national hydrography dataset (NHD). The similarity between perennial stream density and runoff coefficient is promising based on the case study watersheds. As a potential application for macroscale hydrological modeling, perennial stream density in ungauged basin can be predicted based on climate aridity index using the complementary Budyko curve.