Emerging applications involving device-to-device communication among wearable electronics require gigabits per second throughput, which can be achieved by utilizing millimeter-wave (mmWave) frequency bands. When many such communicating devices are indoors in close proximity, such as in a train, car, or airplane cabin, interference can be a serious impairment. This paper uses stochastic geometry to analyze the performance of mmWave networks with a finite number of interferers in a finite network region. Prior work considered either lower carrier frequencies with different antenna and channel assumptions, or a network with an infinite spatial extent. In this paper, human users not only carry potentially interfering devices, but also act to block interfering signals. Using a sequence of simplifying assumptions, accurate expressions for coverage and rate are developed that capture the effects of key antenna characteristics, such as directivity and gain, and are a function of the finite area and number of users. The assumptions are validated through a combination of analysis and simulation. The main conclusions are that mmWave frequencies can provide gigabits per second throughput even with omni-directional transceiver antennas, and larger, more directive antenna arrays give better system performance.