  We present a new formula for the rate at which cosmic strings lose energy
into gravitational radiation, valid for all piecewise-linear cosmic string
loops. At any time, such a loop is composed of $N$ straight segments, each of
which has constant velocity. Any cosmic string loop can be arbitrarily-well
approximated by a piecewise-linear loop with $N$ sufficiently large. The
formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the
effects of gravitational back-reaction are neglected. For a given loop, the
large number of terms makes evaluation ``by hand" impractical, but a computer
or symbolic manipulator yields accurate results. The formula is more accurate
and convenient than previous methods for finding the gravitational radiation
rate, which require numerical evaluation of a four-dimensional integral for
each term in an infinite sum. It also avoids the need to estimate the
contribution from the tail of the infinite sum. The formula has been tested
against all previously published radiation rates for different loop
configurations. In the cases where discrepancies were found, they were due to
errors in the published work. We have isolated and corrected both the analytic
and numerical errors in these cases. To assist future work in this area, a
small catalog of results for some simple loop shapes is provided.
