It is known that there is a lag time for smoke plume induced by fires transporting from a fire origin to the location of interest underneath an unconfined and flat ceiling.This lag behavior of smoke plume also exists for a fire under a sloped ceiling,and is fundamental to estimate the activation time of a fire detector or other fire extinguishing system.This study focuses on the lag time of smoke plume under a sloped ceiling.Based on the weak-plume theory at early-fire phase and previous studies concerning the fire plume characteristics under a sloped ceiling,a calculation method on lag time of fire plume transporting is presented in theory.Meanwhile,two dimensionless equations predicting the lag time of fire plume for steady fire and unsteady fire are proposed respectively.Furthermore,the critical time calculation equation is also proposed to determine the applicability of quasi-steady assumption for a time-dependent fire. It is known that there is a lag time for smoke plume induced by fires transporting from a fire origin to the location of interest underneath an unconfined and flat ceiling.This lag behavior of smoke plume also exists for a fire under a sloped ceiling, and is fundamental to estimate the activation time of a fire detector or other fire extinguishing system. This study focuses on the lag time of smoke plume under a sloped ceiling. Based on the weak-plume theory at early-fire phase and previous studies concerning the fire plume characteristics under a sloped ceiling, a calculation method on lag time of fire plume transporting is presented in theory. However, two dimensionless equations predicting the lag time of fire plume for steady fire and unsteady fire are are respectively respectively.Furthermore, the critical time calculation equation is also proposed to determine the applicability of quasi-steady-state for a time-dependent fire.