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 was proposed. The central position estimator designed using the dynamic average consensus algorithm enabled each agent to obtain the geometric center of multiple dynamic target positions. The surrounding radius estimator, designed using a dynamic maximum consensus algorithm, enabled each agent to estimate formation vector with optimal encirclement radius in real-time through a distributed approach. Integrating the concept of "holistic planning and segmented control," the study considered both spatial and temporal dimensions, achieving specified-time-area surrounding formation under the framework. The ability to achieve zero steady-state formation error within a specified time was proven using algebraic graph theory and Lyapunov function theory. Simulation experiments validate the effectiveness and accuracy of the algorithm.