X-ray spectra of quiescent low-mass X-ray binaries containing neutron stars can be fit with atmosphere models to constrain the mass and the radius. Mass-radius constraints can be used to place limits on the equation of state of dense matter. We perform fits to the X-ray spectrum of a quiescent neutron star in the globular cluster M13, utilizing data from ROSAT, Chandra, and XMM–Newton, and constrain the mass–radius relation. Assuming an atmosphere composed of hydrogen and a 1.4 M_⊙ neutron star, we find the radius to be $$R_{\rm NS}=12.2^{+1.5}_{-1.1}$$ km, a significant improvement in precision over previous measurements. Incorporating an uncertainty on the distance to M13 relaxes the radius constraints slightly and we find $$R_{\rm NS}=12.3^{+1.9}_{-1.7}$$ km (for a 1.4M_⊙ neutron star with a hydrogen atmosphere), which is still an improvement in precision over previous measurements, some of which do not consider distance uncertainty. We also discuss how the composition of the atmosphere affects the derived radius, finding that a helium atmosphere implies a significantly larger radius.