The ability to convert spin accumulation to charge currents is essential for applications in spintronics. In semiconductors, spin-to-charge conversion is typically achieved using the inverse spin Hall effect or using a large magnetic field. Here we demonstrate a general method that exploits the nonlinear interactions between spin and charge currents to perform all-electrical, rapid, and noninvasive detection of spin accumulation without the need for a magnetic field. We demonstrate the operation of this technique with ballistic GaAs holes as a model system with strong spin-orbit coupling, in which a quantum point contact provides the nonlinear energy filter. This approach is generally applicable to electron and hole systems with strong spin-orbit coupling.