Scientists' ability to integrate diverse forms of evidence and evaluate how well they can explain and predict phenomena, in other words, $\textit{to know how much they know}$, struggles to keep pace with technological innovation. Central to the challenge of extracting knowledge from data is the need to develop a metric of knowledge itself. A candidate metric of knowledge, $K$, was recently proposed by the author. This essay further advances and integrates that proposal, by developing a methodology to measure its key variable, symbolized with the Greek letter $\tau$ ("tau"). It will be shown how a $\tau$ can represent the description of any phenomenon, any theory to explain it, and any methodology to study it, allowing the knowledge about that phenomenon to be measured with $K$.To illustrate potential applications, the essay calculates $\tau$ and $K$ values of: logical syllogisms and proofs, mathematical calculations, empirical quantitative knowledge, statistical model selection problems, including how to correct for "forking paths" and "P-hacking" biases, randomised controlled experiments, reproducibility and replicability, qualitative analyses via process tracing, and mixed quantitative and qualitative evidence.Whilst preliminary in many respects, these results suggest that $K$ theory offers a meaningful understanding of knowledge, which makes testable metascientific predictions, and which may be used to analyse and integrate qualitative and quantitative evidence to tackle complex problems.