We present an atomic cluster expansion (ACE) for carbon that improves over available classical and machine learning potentials. The ACE is parametrized from an exhaustive set of important carbon structures over extended volume and energy ranges, computed using density functional theory (DFT). Rigorous validation reveals that ACE accurately predicts a broad range of properties of both crystalline and amorphous carbon phases while being several orders of magnitude more computationally efficient than available machine learning models. We demonstrate the predictive power of ACE on three distinct applications: brittle crack propagation in diamond, the evolution of amorphous carbon structures at different densities and quench rates, and the nucleation and growth of fullerene clusters under high-pressure and high-temperature conditions.