Invisible is a musical re-telling of H.G. Wells' classic sci-fi novel The Invisible Man, by way of John Hughes. It tells the story of Griffin and Kemper, who, much to the chagrin of their goth friend Hemlock, attempt to win the hands of the popular queens of the school, Tiffany Madison and Tiffany Melrose, using nothing but their nerdy wits and scientific know-how. The two hatch a plan to make themselves popular through science, and even get their trying-way-too-hard-to-be-cool Social Studies teacher, Mr Reeves, to unwittingly help them. However, an accident during the experiment just turns Griff invisible instead.
When Kemper runs afoul of the school's affluent jock bully Chetwick (and his two loyal lieutenants, Craig and Jackal), Griff is forced to use his invisibility to aid Kemper in a fight, which results in Kemper becoming the most popular kid in school overnight. This quickly goes to Kemper's head, and he exhorts Griff to use his invisibility to publicly humiliate Chetwick, in an attempt to secure his place at the top of the social pyramid. Griff thinks this is going too far, which causes a rift between the two and even leads to Kemper publicly betraying Griff, which spurs Griff into enacting a reign of terror. (End of Act 1)
Griff becomes a kind of urban legend, menacing Kemper and the school at large with invisible antics and science-based pranks. As Hemlock searches the school for Griff, she runs into Craig and Mr. Reeves, who recounts the story of his unrequited high school crush. Hemlock begins to realize she has feelings for Griff that she’s been avoiding, and Craig realizes that he has feelings for Chetwick. As Hemlock admonishes Craig to express his feelings, which takes Mr. Reeves by surprise, she also realizes that Griff shows up in the photographs she’s taken of him. She goes to tell Griff, but the conversation derails when it’s revealed that Griff plans to exact poetic justice by using the invisibility serum on Kemper at the moment that he is crowned prom king. Meanwhile, Craig confesses his feelings to Chetwick. Chetwick can't deal with these emotions, and leaves.
At the prom, Kemper, now worn down by guilt and the pressures of popularity, refuses the title of prom king. Griff, who has arrived just in time to see this, decides to push him out of the way of the serum and is hit by it instead. When the serum turns him visible again, Griff uses the attention to publicly apologize to Hemlock for all he’s put her through, and expresses that he has feelings for her, as well. Hemlock explains that she snuck some photo development fluid into the serum. Meanwhile, Chetwick finally returns Craig’s affections, Mr. Reeves resolves to move on past his high school crush, and Griff and Kemper reconcile, just as the last dance of prom begins.