Vibrotactile rendering is an emerging interaction method for information transmission in mobile devices, replacing or supplementing visual and auditory displays. To design effective vibrotactile actuators or display algorithms, an understanding of the perceived intensity (strength) of their vibrations is essential. This paper aims to build a robust model for the perceived intensities of mobile device vibrations, which can be immediately used by engineers and application designers. To this end, we carried out two psychophysical experiments using absolute magnitude estimation procedures. In Experiment I, we investigated the effects of vibration direction and device weight on the perceived intensity of mobile device vibrations. The vibration directions tested (height, width, and depth), and the device weights (90-130 g) were determined considering those of contemporary mobile devices. Only the vibration direction was found to be a statistically significant factor, showing the highest perceived intensities along the height direction of a mobile device. In Experiment II, we measured the perceived intensities of vibrations with various amplitudes and frequencies along the three vibration directions. Then, for each direction, a psychophysical magnitude function and equal sensation contours were constructed based on Stevens' power law, which clearly visualize the consequences of vibration parameter changes on the resulting perceptual strength. In addition, we found a monotonic relationship between the physical power of vibration absorbed by the hand and the resulting perceived intensity. This suggests that the former, which is greatly easier to acquire in practice, is a reliable predictor of the latter. We expect that the results of this study can provide immediate knowledge about the perceptual strength of vibrations that engineers and applications developers will find useful.