We show that visual acuity in humans is limited by the amount of primary visual cortex (V1) devoted to a region of the visual field, called the linear cortical magnification factor (M). We used fMRI to measure M in V1, and two psychophysical tasks to measure acuity (Vernier and grating) in the same ten observers. Across observers, the decrease in M with increasing eccentricity predicts the corresponding decrease in acuity for both tasks. Furthermore, observers with lower grating acuity thresholds, measured with laser interferometry, had a significantly greater overall M. These results establish faithful estimates of cortical limits to visual acuity.