We argue that the Square Kilometre Array has the potential to make both redshift ( HI ) surveys and radio continuum surveys that will revolutionize cosmological studies , provided that it has sufficient instantaneous field-of-view that these surveys can cover a hemisphere ( f _ { sky } \sim 0.5 ) in a timescale \sim 1 ~ { } yr . Adopting this assumption , we focus on two key experiments which will yield fundamental new measurements in cosmology , characterizing the properties of the mysterious dark energy which dominates the dynamics of today ’ s Universe . Experiment I will map out \sim 10 ^ { 9 } ( f _ { sky } / 0.5 ) HI galaxies to redshift z \approx 1.5 , providing the premier measurement of the clustering power spectrum of galaxies : accurately delineating the acoustic oscillations and the ‘ turnover ’ . Experiment II will quantify the cosmic shear distortion of \sim 10 ^ { 10 } ( f _ { sky } / 0.5 ) radio continuum sources , determining a precise power spectrum of the dark matter , and its growth as a function of cosmic epoch . We contrast the performance of the SKA in precision cosmology with that of other facilities which will , probably or possibly , be available on a similar timescale . We conclude that data from the SKA will yield transformational science as the direct result of four key features : ( i ) the immense cosmic volumes probed , exceeding future optical redshift surveys by more than an order of magnitude ; ( ii ) well-controlled systematic effects such as the narrow ‘ k -space window function ’ for Experiment I and the accurately-known ‘ point-spread function ’ ( synthesized beam ) for Experiment II ; ( iii ) the ability to measure with high precision large-scale modes in the clustering power spectra , for which nuisance effects such as non-linear structure growth , peculiar velocities and ‘ galaxy bias ’ are minimised ; and ( iv ) different degeneracies between key parameters to those which are inherent in the Cosmic Microwave Background .