We investigate the flow generated by a magnetic stirrer in cylindrical containers by optical observations, particle image velocimetry measurements, and particle and dye tracking methods. The tangential flow is that of an ideal vortex outside a core, but inside downwelling occurs with a strong jet in the very middle. In the core region dye patterns remain visible over minutes indicating inefficient mixing in this region. The results of quantitative measurements can be described by simple relations that depend on the stirring bar’s rotation frequency. The tangential flow is similar to that of large atmospheric vortices such as dust devils and tornadoes.