The multivariate Oja (1983) median is an affine equivariant multivariate location estimate with high efficiency. This estimate has a bounded influence function but zero breakdown. The computation of the estimate appears to be highly intensive. We consider different, exact and stochastic, algorithms for the calculation of the value of the estimate. In the stochastic algorithms, the gradient of the objective function, the rank function, is estimated by sampling observation hyperplanes. The estimated rank function with its estimated accuracy then yields a confidence region for the true Oja samplemedian, and the confidence region shrinks to the sample median with the increasing number of the sampled hyperplanes. Regular grids and and the grid given by the data points are used in the construction. Computation times of different algorithms are discussed and compared. Computation of the multivariate Oja median