  We derive fundamental limits on measurements of position, arising from
quantum mechanics and classical general relativity. First, we show that any
primitive probe or target used in an experiment must be larger than the Planck
length, $l_P$. This suggests a Planck-size {\it minimum ball} of uncertainty in
any measurement. Next, we study interferometers (such as LIGO) whose precision
is much finer than the size of any individual components and hence are not
obviously limited by the minimum ball. Nevertheless, we deduce a fundamental
limit on their accuracy of order $l_P$. Our results imply a {\it device
independent} limit on possible position measurements.
