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The relative velocity between mobile devices is one of the key factors that determine the quality of communications in Mobile Ad-hoc NETworks (MANETs). Velocity estimates are useful in various aspects of ad hoc networking (e.g., predicting link lifetime and measuring performance). Conventional ways of estimating velocity rely on the availability of positioning systems such as the Global Positioning System (GPS) or precise knowledge of the characteristics of wireless channels/signals. A recently proposed method exploits time-varying internode range information for velocity estimations, provided that the range estimates are noise free. In this paper, we propose a new range-based method for relative velocity estimations (RVEs). We derive two range-based relative velocity estimators for both sparse and dense ad hoc networks, i.e., RVEs and RVEd. In addition to being less dependent on the characteristics of the wireless channel, the proposed method is more tolerant of the multipath or nonline-of-sight (NLOS) errors contained in range measurements than the existing method. Simulation results show an excellent match between the velocity estimates given by the proposed method and the actual values in both sparse and dense network cases, regardless of the nodal speed limits or the distribution of noises. In comparison with the existing method, the proposed method is shown to achieve an improvement factor of about 33 (in terms of normalized bias) with Gaussian multipath noises of 4-m standard deviation or 20 with uniform NLOS noises of 32-m maximum standard deviation.