The existence of a negative static dielectric constant has drawn a great deal of theoretical controversy. Experimentally, one has never been observed. However, low-frequency negative capacitance has been widely reported in fields including physics, chemistry, biology, geology, and electronics. This wide variety of systems possesses an extremely diverse set of physical processes that, surprisingly, share similar characteristics. We present a general mechanism that unites the various instances of negative capacitance under a common framework. The mechanism demonstrates that the negative capacitance arises from dc/ac signal mixing across a nonlinear conductor. Verification of the model is performed in physically distinct samples: an electrorheological fluid, a fuel cell, and a solar cell. Furthermore, we argue that the negative capacitance, under appropriate conditions, can be associated with a negative-differential dielectric constant, possibly even in the static limit.