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Abstract Negative capacitance in BaTiO3/SrTiO3 superlattices is investigated by Monte Carlo simulations in an atomistic effective Hamiltonian model, using fluctuation formulas for responses to the local macroscopic field that incorporates depolarizing fields. We show that epitaxial strain can tune the negative capacitance of the BaTiO3 ferroelectric layer and the overall capacitance of the system. In addition, we predict and explain an original switching of the negative capacitance from the BaTiO3 layer to the SrTiO3 layer at low temperatures for intermediate strains.