Equation for predicting contrail formation
Schmidt-Appleman criterion (SAC) is used to model contrail formation. I advise reading in full Ulrich Schumann's article "A contrail cirrus prediction model" (http://www.geosci-model-dev.net/5/543/2012/gmd-5-543-2012.pdf) to get all the relevant formulae and literature references.

While it is possible to transcribe the formulae here, the reference cited does a better job of presenting state of the art (2012).