  Light at a magic-zero wavelength causes zero energy shift for an atom. We
measured the longest magic-zero wavelength for ground state potassium atoms to
be $\lambda_\textrm{zero}=768.971(1)$ nm, and we show how this provides an
improved experimental benchmark for atomic structure calculations. This
$\lambda_\textrm{zero}$ measurement determines the ratio of the potassium atom
D1 and D2 line strengths with record precision. It also demonstrates a new
application for atom interferometry, and we discuss how decoherence will
fundamentally limit future measurements of magic-zero wavelengths.
