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The Kepler space telescope leaves a legacy of tens of thousands of stellarrotation period measurements. While many of these stars show strongperiodicity, there exists an even bigger fraction of stars with irregularvariability for which rotation periods are unknown. As a consequence, manystellar activity studies might be strongly biased toward the behavior of moreactive stars with measured rotation periods. To at least partially lift thisbias, we apply a new method based on the Gradient of the Power Spectrum (GPS).The maximum of the gradient corresponds to the position of the inflection point(IP). It was shown previously that the stellar rotation period $P_{rot}$ islinked to the inflection point period $P_{IP}$ by the simple equation $P_{rot}= P_{IP}/\alpha$, where $\alpha$ is a calibration factor. The GPS method issuperior to classical methods (such as auto-correlation functions (ACF))because it does not require a repeatable variability pattern in the timeseries. From the initial sample of 142,168 stars with effective temperature$T_{eff}\leq6500K$ and surface gravity $log g\geq4.0$ in the Kepler archive, wecould measure rotation periods for 67,163 stars by combining the GPS and theACF method. We further report the first determination of a rotation period for20,397 stars. The GPS periods show good agreement with previous periodmeasurements using classical methods, where these are available. Furthermore,we show that the scaling factor $\alpha$ increases for very cool stars witheffective temperatures below 4000K, which we interpret as spots located athigher latitudes. We conclude that new techniques (such as the GPS method) mustbe applied to detect rotation periods of stars with small and more irregularvariabilities. Ignoring these stars will distort the overall picture of stellaractivity and, in particular, solar-stellar comparison studies.

New rotation period measurements of 67,163 Kepler stars