  It has been previously shown that a particular nonperturbative
constituent-quark model of hadrons describes experimental measurements of
electromagnetic form factors of light charged mesons through a small number of
common phenomenological parameters, matching at the same time the
Quantum-Chromodynamics (QCD) asymptotics for the pi-meson form factor at large
momentum transfer. Here we start with the determination of the K0
electromagnetic form factor in this approach. Precise measurement of the K0
charge radius makes it possible to constrain model parameters with high
accuracy. Then, with all parameters fixed, we revisit the K+ form factor and
find that it matches experimental measurements in the infrared, lattice results
at moderate momentum transfer and the perturbative QCD asymptotics in the
ultraviolet. In this way we obtain a narrow constraint on the K+ charge radius,
<r_K+^2> = 0.403 +0.007 -0.006 fm^2, and extend the successful
infrared-ultraviolet connection from pi to K mesons.
