Existing grasp synthesis methods are either analytical or data-driven. The former one is oftentimes limited to specific application scope. The latter one depends heavily on demonstrations, thus suffers from generalization issues; e.g., models trained with human grasp data would be difficult to transfer to 3-finger grippers. To tackle these deficiencies, we formulate a fast and differentiable force closure estimation method, capable of producing diverse and physically stable grasps with arbitrary hand structures, without any training data. Although force closure has commonly served as a measure of grasp quality, it has not been widely adopted as an optimization objective for grasp synthesis primarily due to its high computational complexity; in comparison, the proposed differentiable method can test a force closure within 4ms. In experiments, we validate the proposed method’s efficacy in 8 different settings.