In light of recent growth in privacy awareness and data ownership rights, differential privacy (DP) has emerged as a promising technique employed by several well-known data controller entities. This raises the question of how casual users, as the immediate recipients of privacy threats and risks, comprehend and perceive DP and its key parameter ε, as DP’s provided protection depends on it. Existing studies show that ordinary users have the potential to understand the fundamental mechanism of DP and its implications for the privacy-utility trade-off when they are communicated clearly through textual and visual aids and, accordingly, make informed decisions about sharing their data under differential privacy protection. However, these attempts either only implicitly mention a few possible values for ε, such as low, medium, and high, or altogether leave it out of the communication. In this paper, we conduct a between-subject user study (N = 426) to investigate the effectiveness of nine interactive visual tools to communicate ε explicitly and on a continuous scale in a data-sharing scenario related to publishing positive COVID-19 test results. These interactive visual tools allow casual users to visualize DP’s effects on data accuracy and/or privacy loss for various ε values. We found that visualizations incorporating the privacy loss component have a significant impact on assisting users in selecting values that are closer to the recommended values by experts. However, depending on the ratio between DP noise and underlying data, the accuracy loss component disparately affects users’ ε decision; the bigger the relative error, the bigger the selected epsilon and vice versa. Thus, accuracy portrayals should be carried out with care. We contextualize our findings in the existing literature and conclude with insights and recommendations on effectively employing our findings to communicate differential privacy to casual users.