  We determine the ratio FK/Fpi in QCD with Nf=2+1 flavors of sea quarks, based
on a series of lattice calculations with three different couplings, large
volumes and a simulated pion mass reaching down to about 190 MeV. We obtain
FK/Fpi = 1.192 +- 0.007(stat) +- 0.006(sys) with all the sources of systematic
uncertainty under control.
