  We provide a general framework of estimates for convergence rates of random
discrete model curves approaching Schramm Loewner Evolution (SLE) curves in the
lattice size scaling limit. We show that a power-law convergence rate of an
interface to an SLE curve can be derived from a power-law convergence rate for
an appropriate martingale observable provided the discrete curve satisfies a
specific bound on crossing events, the Kempannien-Smirnov condition, along with
an estimate on the growth of the derivative of the SLE curve. We apply our
framework to show that the exploration process for critical site percolation on
hexagonal lattice converges to the SLE$_6$ curve with a power-law convergence
rate.
