We present an explicit method for simulating origami that can be rapidly computed on a Graphics Processing Unit (GPU). Previous work on origami simulation methods model the geometric or structural behaviors of origami with a focus on physical realism; in this paper we introduce a compliant, explicit numerical simulation method that emphasizes computational speed and interactivity. We do this by reformulating existing techniques for simulating origami so that they can be computed on highly parallel GPU architectures. We implement this method in an open-source, GPU-accelerated WebGL app that runs in any modern browser. We evaluate our method’s performance, stability, and scalability to existing methods (Freeform Origami, MERLIN) and demonstrate its capacity for real-time interaction through a traditional GUI and immersive virtual reality.