Storing, transmitting, and manipulating information using the electron spin resides at the heart of spintronics. Fundamental for future spintronics applications is the ability to control spin currents in solid state systems. Among the different platforms proposed so far, semiconductors with strong spin-orbit interaction are especially attractive as they promise fast and scalable spin control with all-electrical protocols. Here we demonstrate both the generation and measurement of pure spin currents in semiconductor nanostructures. Generation is purely electrical and mediated by the spin dynamics in materials with a strong spin-orbit field. Measurement is accomplished using a spin-to-charge conversion technique, based on the magnetic field symmetry of easily measurable electrical quantities. Calibrating the spin-to-charge conversion via the conductance of a quantum point contact, we quantitatively measure the mesoscopic spin Hall effect in a multiterminal GaAs dot. We report spin currents of 174 pA, corresponding to a spin Hall angle of 34%.The generation and detection of spin currents in nanostructures is the central challenge of semiconductor spintronics. On the one hand, spin injection cannot be easily achieved by coupling semiconductors to ferromagnets [1] because of the lack of control over material interfaces [2]. On the other hand, magnetoelectric alternatives exploiting the celebrated spin Hall effect (SHE) [3,4], have delivered only qualitative measurement protocols in transport experiments [5]. Alternatively to all-electrical setups, spin polarizing the current through a quantum point contact (QPC) with a magnetic field allows a quantitative control over spin current generation and detection at the nanoscale [6][7][8]. The latter approach typically requires such high magnetic fields (6 − 8 Tesla) that, as a drawback, the desired magnetoelectric effects are either suppressed or totally altered. This Letter reports two major advances of nanoscale semiconductor spintronics. Namely, we develop novel experimental methods to electrically generate and quantitatively measure spin currents in a two-dimensional semiconductor nanostructure.It is predicted that charge currents flowing through spin-orbit interaction (SOI)-coupled nanostructures are generically accompanied by spin currents, if the spinorbit time is shorter than the electron dwell time [9][10][11][12]. This spin current generation mechanism is purely electrical and based on the mesoscopic SHE (MSHE) [9,10], where the electronic orbital dynamics in chaotic nanostructures cooperates with the SOI to make transport spin dependent. We will consider an open three-terminal quantum dot as represented in Fig. 1(a), where each lead i is a QPC carrying N i spin degenerate modes. Running a charge current I between terminals 1 and 2, a spin current in all terminals, including 3, is expected due to the MSHE.For a weak SOI, the spin currents' amplitude fluctuates from sample to sample with zero average. For cavities with a strong SOI, geometric correlations between ...