The uncertainties in both the position of a pole of rotation and the rotation angle describing a plate reconstruction depend not only on the number and quality of data used but also on two geometrical factors: the length of plate boundary represented by the data, and the distance from the best-fit pole to the center of the data region. We describe a simple geometrical method that can be used to calculate minimum uncertainties in reconstructions, based on positions of magnetic anomalies and fracture zones with finite uncertainties. Uncertainties in pole positions and angles corresponding to 10-km uncertainty in individual data points can, when combined, yield uncertainties in reconstructed positions greatly in excess of 10 km per rotation. For example, an uncertainty of 10 km in anomaly 6 reconstructions in the South Pacific, southeast Indian, northwest Indian, and North Atlantic Oceans would result in uncertainty of up to 190 km in the reconstructed position of the Pacific plate with respect to North America at 19.8 m.y. B.P. Existing data show that the realistic uncertainties for this case are twice as large as the calculated minimum uncertainties.