Soft wearable robotic hand can assist with hand function for the performance of activities of daily living (ADL). However, existing robotic hands lack a mathematical way to quantify the grip force generated for better controlling the grasp of objects during the performance of ADL. To address this issue, this article presents a soft wearable robotic hand with active control of finger flexion and extension through an elastomeric-based bi-directional soft actuator. This actuator bends and extends by pneumatic actuation at lower air pressure, and a flex sensor embedded inside the actuator measures the angles of the fingers in real-time. Analytical models are established to quantify the kinematic and tip force for gripping of the actuator in terms of the relationship between the input pressure and the bending angle, as well as the output force, and are validated experimentally and by the finite element method. Furthermore, the ability of the soft robotic hand to grasp objects is validated with and without being worn on a human hand. The robotic hand facilitates hand opening and closing by the wearer and successfully assists with grasping objects with sufficient force for ADL-related tasks, and the grip force provided by the actuator is further estimated by the analytical models on two healthy subjects. Results suggest the possibility of the soft robotic hand in providing controllable grip strength in rehabilitation and ADL assistance.