The prediction of unstart boundaries of hypersonic inlets is significant to the engine control. To correct the previous conclusions based on the one-dimensional and inviscid flow assumption, the present paper numerically investigates the unstart characteristics of two-dimensional contraction ducts in viscous flow that vary with multiple controlling variables. Based on the newly defined dimensionless cowl length and effective internal contraction ratio, the similarity law of unstart is discovered. The universal empirical equation of unstart boundary for different cowl lengths, cowl lip heights, entrance boundary-layer thicknesses, unit Reynolds numbers, and Mach numbers is proposed, which can simplify the design of two-dimensional hypersonic inlets. With varying the dimensionless cowl length, three different types of short-cowl, transitional, and long-cowl unstarts are identified, owing to the different evolution mechanisms of separation region. The unstart displays a separation region growing under the streamwise pressure difference enhanced by the shock system or flow choke. In addition, the wall pressure criteria for unstart are correlated to the characteristic separation scale at unstart critical state and the dimensionless cowl length, which facilitates the unstart detection or early warning. It is observed that the Kantrowitz limit is close to the unstart boundaries for very short cowl and the isentropic limit is close to the unstart boundaries for very long cowl. [ABSTRACT FROM AUTHOR]