Although much has been learned about the spatial sampling and filtering properties of peripheral vision, little attention has been paid to the remarkably clear appearance of the peripheral visual field. To study the apparent sharpness of stimuli presented in the periphery, we presented Gaussian blurred horizontal edges at 8.3, 16.6, 24, 32, and 40 deg eccentricity. Observers adjusted the sharpness of a similar edge, viewed foveally, to match the appearance of the peripheral stimulus. All observers matched blurred peripheral stimuli with sharper foveal stimuli. We have called this effect "sharpness overconstancy". For field sizes of 4 deg, there was greater overconstancy at larger eccentricities. Scaling the field size of the peripheral stimuli by a cortical magnification factor produced sharpness overconstancy which was independent of eccentricity. In both cases, there was a slight sharpness underconstancy for peripherally presented edges blurred only slightly. We consider various explanations of peripheral sharpness overconstancy.