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We present a simple parameterization of a running coupling constant, definedvia the static potential, that interpolates between 2-loop QCD in the UV andthe string prediction in the IR. Besides the usual $\Lam$-parameter and thestring tension, the coupling depends on one dimensionless parameter,determining how fast the crossover from UV to IR behavior occurs (in principlewe know how to take into account any number of loops by adding moreparameters). Using a new Ansatz for the LATTICE potential in terms of thecontinuum coupling, we can fit quenched and unquenched Monte Carlo results forthe potential down to ONE lattice spacing, and at the same time extract therunning coupling to high precision. We compare our Ansatz with 1-loop resultsfor the lattice potential, and use the coupling from our fits to quantitativelycheck the accuracy of 2-loop evolution, compare with the Lepage-Mackenzieestimate of the coupling extracted from the plaquette, and determine Sommer'sscale $r_0$ much more accurately than previously possible. For pure SU(3) wefind that the coupling scales on the percent level for $\beta\geq 6$.Comment: 47 pages, incl. 4 figures in LaTeX [Added remarks on correlated vs.  uncorrelated fits in sect. 4; corrected misprints; updated references.

QCD (lattice) potential and coupling: How to accurately interpolate between multiloop QCD and the string picture