Separation of particles is often designed based on the terminal settling velocity as separation parameter. Until now, the particle state of motion is described by solving the force balance equation numerically, which is highly complex. In this work, algebraic equations are presented, which describe the temporal changes of the setting velocity and the displacement at sinking in laminar and turbulent flows around the particle. These equations solely depend upon particle size, density and shape and are independent of the initial velocity. Using the characteristic values, the time period where a sufficient convergence to the terminal sinking velocity is reached, can be clearly identified.