Studies of kaon production in accelerator-based neutrino experiments provide an important constraint on a $K^+$ production by atmospheric neutrinos in proton decay searches. Current neutrino-nucleus event generators largely rely on theoretical models for the descriptions of backgrounds due to kaons and need to be verified by measurements.


At neutrino energies below 2 GeV, the event rate for processes with a $K^+$ production is low as compared to pion production channels because of Cabibbo suppression and the relatively large kaon mass.
At higher neutrino energies, a different production mechanism dominates, where $K^+$ is always accompanied by another strange particle to conserve the strangeness.

T2K searches for charged-current neutrino interactions that produce a $K^+$ in the final state in the
Fine Grained Detector, a scintillator-based tracking calorimeter, within the T2K near detector ND280. Events with a $K^+$ are identified in T2K by studying the energy deposition of tracks in the Time Projection Chamber.
These proceedings discuss the $K^+$ sample selection together with the method used to estimate the backgrounds and evaluate a single-bin cross section.