Addressing the challenges of incompletely distributed formation vector determination and uncertain task completion times in multi-agent systems performing dynamic multi-target encirclement tasks, a specified-time-area surrounding formation control algorithm based on the center position estimator and surrounding radius estimator is proposed. The central position estimator designed using the dynamic average consensus algorithm enables each agent to obtain the geometric center of multiple dynamic target positions. The surrounding radius estimator, designed using a dynamic maximum consensus algorithm, enables each agent to estimate the optimal encirclement radius in real-time through a distributed approach. Integrating the concept of "holistic planning and segmented control," the study considers both spatial and temporal dimensions, achieving specified-time-area surrounding formation. The ability to achieve zero steady-state formation error within a specified time is proven using algebraic graph theory and Lyapunov function theory. Simulation experiments validate the effectiveness and accuracy of the algorithm.