The use of millimeter-wave (mmWave) bandwidth is one key enabler to achieve the high data rates in the fifth-generation (5G) cellular systems. However, mmWave signals suffer from significant path loss due to high directivity and sensitivity to blockages, limiting its adoption within small-scale deployments. To enhance the coverage of mmWave communication in 5G and beyond, it is promising to deploy a large number of reconfigurable intelligent surfaces (RISs) that passively reflect mmWave signals towards desired directions. With this motivation, in this work, we study the coverage of an RIS-assisted large-scale mmWave cellular network using stochastic geometry, and derive the peak reflection power expression of an RIS and the downlink signal-to-interference ratio (SIR) coverage expression in closed forms. These analytic results clarify the effectiveness of deploying RISs in the mmWave SIR coverage enhancement, while unveiling the major role of the density ratio between active base stations (BSs) and passive RISs. Furthermore, the results show that deploying passive reflectors are as effective as equipping BSs with more active antennas in the mmWave coverage enhancement. Simulation results confirm the tightness of the closed-form expressions, corroborating our major findings based on the derived expressions.INDEX TERMS Millimeter-wave (mmWave), reconfigurable intelligent surface (RIS), coverage, signalto-interference ratio (SIR), stochastic geometry.