A light sterile neutrino that mixes with the active states has been proposed to explain anomalies in short baseline neutrino oscillation data. Constraints on the mass and mixing parameters can be presented by showing results from complementary neutrino oscillation experiments. However, measurements of the Cosmic Microwave Background, most recently by the Planck satellite, constrain the radiative degrees of freedom in the early universe, which would be affected by a sterile neutrino. We have translated these Planck constraints from the cosmological parameter space, into the parameter space of neutrino oscillation, that of mixing angles and mass splittings, and vice versa. We show these constraints from Planck compared to the muon-neutrino disappearance oscillation limits on sterile neutrinos from MINOS and IceCube, and also compare them with the recent electron-neutrino disappearance limits from reactor experiments such as Daya Bay and NEOS. Finally we present new results of the cosmological limits in the context of muon-to-electron-neutrino appearance searches.