This paper demonstrates how the computational analysis of Shakespeare’s plays can map the emotional language used across individual plays and across the canon more broadly, affording new insights. It explains how we adapted the “sentiment analysis” tool SentiStrength for use with Early Modern English. Our analyses allow us to test out the long-held critical hypothesis that Shakespeare’s work moved from a comic to a “problem” and tragic period, and thence to a more optimistic redemptive mood in his last plays. The paper will also suggest how computational techniques can further understanding of genre, in particular the relationship between history and tragedy in Shakespeare’s work.