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The Hα emission line in galaxies is a powerful tracer of their recent star formation activity. With the advent of JWST, we are now able to routinely observe Hα in galaxies at high redshift (z ≳ 3) and thus measure their star formation rates (SFRs). However, using classical SFR(Hα) calibrations to derive the SFRs leads to biased results because high-redshift galaxies are commonly characterized by low metallicities and bursty star formation histories, affecting the conversion factor between the Hα luminosity (LHα) and the SFR. We developed a set of new SFR(Hα) calibrations that allowed us to predict the SFRs of Hα-emitters at z ≳ 3 with very little error. We used the SPHINX cosmological simulations to select a sample of star-forming galaxies representative of the Hα-emitter population observed with JWST. We then derived linear corrections to the classical SFR(Hα) calibrations that took variations in the physical properties (e.g., stellar metallicities) among individual galaxies into account. We obtained two new SFR(Hα) calibrations that compared to the classical calibrations reduce the root mean squared error (RMSE) in the predicted SFRs by ΔRMSE ≈ 0.04 dex and ΔRMSE ≈ 0.06 dex, respectively. Using the recent JWST NIRCam/grism observations of Hα-emitters at z ∼ 6, we show that the new calibrations affect the high-redshift galaxy population statistics: (i) the estimated cosmic SFR density decreases by ΔρSFR ≈ 12%, and (ii) the observed slope of the star formation main sequence increases by Δ∂logSFR/∂logM★ = 0.08 ± 0.02.