Comprehensive analysis of online conversations is important for effective user engagement in customer care. However, conventional approaches are not effective in analyzing customer care conversations frequently and thoroughly. In this work, we introduce computational tone-based metrics derived from online conversations for customer care managers to quantify customer satisfaction, customer concerns and agent performance. We present a computational approach that seamlessly incorporates domain-specific tone analysis with product features to enable multi-faceted conversation analysis. These computational results are integrated with interactive visualizations for visual aggregation, summarization and explanation of user engagement in online customer care. We demonstrate the usefulness and effectiveness of our approach through user studies with customer care managers in an enterprise context.