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We present a new formula for the rate at which cosmic strings lose energyinto gravitational radiation, valid for all piecewise-linear cosmic stringloops. At any time, such a loop is composed of $N$ straight segments, each ofwhich has constant velocity. Any cosmic string loop can be arbitrarily-wellapproximated by a piecewise-linear loop with $N$ sufficiently large. Theformula is a sum of $O(N^4)$ polynomial and log terms, and is exact when theeffects of gravitational back-reaction are neglected. For a given loop, thelarge number of terms makes evaluation ``by hand" impractical, but a computeror symbolic manipulator yields accurate results. The formula is more accurateand convenient than previous methods for finding the gravitational radiationrate, which require numerical evaluation of a four-dimensional integral foreach term in an infinite sum. It also avoids the need to estimate thecontribution from the tail of the infinite sum. The formula has been testedagainst all previously published radiation rates for different loopconfigurations. In the cases where discrepancies were found, they were due toerrors in the published work. We have isolated and corrected both the analyticand numerical errors in these cases. To assist future work in this area, asmall catalog of results for some simple loop shapes is provided.Comment: 29 pages TeX, 16 figures and computer C-code available via anonymous  ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-10,  (section 7 has been expanded, two figures added, and minor grammatical  changes made.

Closed-form expression for the gravitational radiation rate from cosmic strings