Since the posttranscriptional stabilization of β-catenin outside of the cadherin complex appears universally required for β-catenin signaling, the following method allows for simple assessment of the cadherin-free fraction of β-catenin in cells, using a GST-tagged form of ICAT (Inhibitor of β-Catenin and Tcf) as an affinity matrix. 
GST-tagged form of ICAT
Although a number of established techniques and reagents are available to quantify the nuclear signaling activity of β-catenin (e.g., TCF-dependent reporter assays, nuclear accumulation of β-catenin, and generation of N-terminally hypophosphorylated β-catenin), there are cell-type and context-dependent limitations of these methods. 
TCF-dependent reporter assays
Although a number of established techniques and reagents are available to quantify the nuclear signaling activity of β-catenin (e.g., TCF-dependent reporter assays, nuclear accumulation of β-catenin, and generation of N-terminally hypophosphorylated β-catenin), there are cell-type and context-dependent limitations of these methods. 
nuclear accumulation of β-catenin
Although a number of established techniques and reagents are available to quantify the nuclear signaling activity of β-catenin (e.g., TCF-dependent reporter assays, nuclear accumulation of β-catenin, and generation of N-terminally hypophosphorylated β-catenin), there are cell-type and context-dependent limitations of these methods. 
generation of N-terminally hypophosphorylated β-catenin