Three social castes in turn-of-the-century New York introduce themselves to the audience: the first is an upper-class white family from New Rochelle— the Little Boy, Edgar, and his Father (who runs a fireworks factory), Mother, Mother's Younger Brother, and Grandfather—who live a genteel life and enjoy a lack of racial and ethnic diversity; the second is the Black residents of Harlem, including a beautiful young woman named Sarah, who adores the pianist Coalhouse Walker Jr.; the third are immigrants from Europe in the Lower East Side, among them "Tateh", a Jewish artist from Latvia, and his young daughter. These three worlds are connected by narration from the luminaries J. P. Morgan, Henry Ford, Booker T. Washington, Emma Goldman, Harry Houdini, and Evelyn Nesbit (“Prologue—Ragtime”).
Mother bids goodbye to Father as he embarks on Robert Peary's expedition to the North Pole. He asks Mother to oversee his affairs and assures her that nothing will change in his absence, but Mother feels adrift without her husband to guide her (“Goodbye, My Love”). As Peary's ship departs, Father watches as a "rag ship" arrives, carrying a hopeful Tateh and his Little Girl to America, while Mother, back on shore, wishes Father safe passage (“Journey On”). Meanwhile, Mother's Younger Brother, an intense and awkward young man yearning for purpose who works at Father's fireworks factory, attends the vaudeville act of Evelyn Nesbit, a young woman who became famous after her wealthy lover Stanford White was killed by her millionaire husband Harry K. Thaw (“Crime of the Century”). After the show ends, Younger Brother confesses his love to Evelyn. She kisses him, but only for the benefit of a press photographer, and cheerfully rejects him afterward.
Back at home in New Rochelle, Mother discovers a Black newborn partly buried alive in her garden. The police arrive with Sarah, the baby's mother. Pitying her, Mother takes responsibility for Sarah and her child. Surprised at herself, she remarks that her husband would never have allowed her to make such a decision (“What Kind of Woman”).
At Ellis Island, the immigrants arrive (“A Shtetl Iz Amereke”). Tateh eagerly begins his new life, drawing silhouettes and selling them on the street. He and the Little Girl quickly descend into poverty. Emma Goldman attempts to get him to join the Socialist movement, but he refuses. A wealthy man even offers to purchase the Little Girl, whom he now keeps on a leash for safety. Inspired by immigrant magician Harry Houdini, Tateh resolves to begin again somewhere else (“Success”).
In Harlem, Coalhouse, a popular pianist, informs his audience that he's finally found his lost love, Sarah, and is going to win her back (“His Name Was Coalhouse”/“Gettin' Ready Rag”). He then purchases a Model T while Henry Ford and his workers glorify industry (“Henry Ford”).
Tateh and the Little Girl leave for Boston; en route, they meet Mother and Edgar while stopping in New Rochelle. They politely make conversation (“Nothing Like the City”). In the attic of Mother's home, Sarah explains her desperate actions in a song to her baby (“Your Daddy's Son”). Also en route to New Rochelle, Coalhouse is harassed by a racist fire squad led by chief Will Conklin, who taunt him for driving his own car. He arrives at Mother's house, where he has heard that a Black woman is living. He is stunned to learn of the baby's existence and, when Sarah refuses to see him, he resorts to returning weekly (“The Courtship”) until Mother invites him inside. Grandfather asks Coalhouse to play a minstrel song on the parlor piano; instead, Coalhouse plays a ragtime song. Father returns home while Coalhouse is playing, and is stunned by the changes to his family's life, while Mother and her Younger Brother are proud of her choices. Eventually, Sarah comes down from the attic and reconciles with Coalhouse (“New Music”). The two go on an idyllic picnic where, inspired by the words of Booker T. Washington, he dreams of a just, future America that their son will grow up in (“Wheels of a Dream”).
Taking refuge from a wintry night, Younger Brother enters a workers' hall. There, Emma Goldman speaks passionately about a textile mills strike in Lawrence, Massachusetts, where Tateh and his daughter are among those targeted by federal troops and strikebreakers. Younger Brother imagines Goldman is speaking directly to him (“The Night That Goldman Spoke at Union Square”). Goldman is arrested prompting a riot that mirrors the chaos in Lawrence, where Tateh is beaten by a policeman while trying to flee. He and the Little Girl escape Lawrence on a train; he gives his daughter a flip book of moving silhouettes to calm her. The train conductor offers to buy the book, and Tateh, hurriedly dubbing it a "movie-book", sells it for a dollar. Tateh realizes that "movie-books" may be a route out of poverty (“Gliding”).
Returning to New Rochelle, Coalhouse and Sarah are stopped by Will Conklin and the fire squad. Conklin demands a fictitious toll; Coalhouse refuses. A lecture by Booker T. Washington on patience and dignity ironically underscores the white firemen's destruction of Coalhouse's new Model T (“The Trashing of the Car”). Incensed, Coalhouse vows legal action (“Justice”), postponing his marriage to Sarah until he gets justice. Sarah hears of a campaign rally nearby and goes to ask for help from the vice presidential candidate; as she approaches, an onlooker shouts "She's got a gun!" and Sarah is beaten to death by the Secret Service (“President”). At her funeral, Black mourners demand an end to such injustice and pray for true equality. Mother, Father, Younger Brother, Tateh and Emma Goldman look on as Coalhouse weeps at Sarah's grave (“Till We Reach That Day”).
The Little Boy wakes up screaming from a nightmare in which Harry Houdini attempts a daring escape after being locked in a dynamite-laden box by Will Conklin ("Harry Houdini, Master Escapist"). This dream proves prophetic: news arrives that a volunteer firehouse has been bombed. Coalhouse has vowed to get justice on his own terms (“Coalhouse's Soliloquy”) and now terrorizes New Rochelle while demanding his car be restored to him and that Will Conklin be delivered to him. Booker T. Washington condemns Coalhouse's actions (“Coalhouse Demands”). In the chaos, Mother retains custody of Sarah and Coalhouse's baby. Father blames her for bringing this turmoil into their lives, but Younger Brother lambastes him for his blindness and storms out of the house. Mother grows increasingly offended by her husband's ignorant outlook. Father, to distract Edgar from the unrest, takes his son to a baseball game (“What a Game”). Coalhouse's campaign continues (“Fire in the City”), and so Father decides to move the family to Atlantic City.
In Atlantic City, Evelyn Nesbit's career is on the downslide and Harry Houdini has becoming intrigued by the supernatural and the afterlife following the death of his mother (“Atlantic City”). Edgar cryptically shouts "Warn the Duke!" to Houdini. Mother encounters Tateh again, not recognizing him from their brief meeting months ago; now a filmmaker, he has re-invented himself as "the Baron Ashkenazy" and is directing a silent movie in Atlantic City (“Buffalo Nickel Photoplay, Inc.”). Edgar and the Little Girl soon become fast friends, prompting Mother and Tateh to become friends as well; eventually, Tateh reveals who he is, and they grow even closer (“Our Children”).
Back in Harlem, Younger Brother seeks out Coalhouse but is repeatedly turned away until Coalhouse is convinced that he can be trusted. Coalhouse has banished music from his life but watches a carefree young couple ("Harlem Nightclub") and recalls meeting Sarah (“Sarah Brown Eyes”). Younger Brother meets with him but is inarticulate and nervous: his profound thoughts, narrated to the audience by Emma Goldman, stand in contrast to the only phrase he can muster: "I know how to blow things up." (“He Wanted to Say”). With Younger Brother's help, Coalhouse and his men take over J.P. Morgan's magnificent library in the heart of New York City, threatening to blow it up. Father is summoned to help reason with Coalhouse. Before he goes, he assures Mother that everything will soon return to the way it was, but Mother knows such hopes are naive (“Back to Before”). Meeting with the police, Father devises a mediation strategy involving Booker T. Washington, whom Coalhouse allows to enter the library. Washington, invoking the violent legacy Coalhouse is leaving his son, works out a deal with Coalhouse. Younger Brother is enraged at Coalhouse's abandonment of their cause (“Look What You've Done”).
Washington leaves and Father enters the library as a hostage. There, he finally realizes the profundity of society's troubles while seeing Coalhouse convince Younger Brother and his men that violence cannot solve injustice. Coalhouse exhorts them to fight through the power of their words (“Make Them Hear You”). Coalhouse's sacrifice and oratory convince Younger Brother and the men to leave while Father tells Coalhouse about his son. Coalhouse thanks Father for his kindness. Once he leaves the library, Coalhouse is shot dead by the police.
Edgar appears to introduce the Epilogue. Younger Brother departs for Mexico to fight for Emiliano Zapata. Emma Goldman is arrested and deported. Booker T. Washington establishes the Tuskegee Institute, while Evelyn Nesbitt fades into obscurity. Harry Houdini realizes upon the assassination of Archduke Franz Ferdinand that Edgar's shout of "Warn the Duke!" was a true mystical experience. Father dies abord the RMS Lusitania; after a year of mourning, Mother marries Tateh, adopts Coalhouse and Sarah's son, and moves to California. Tateh is struck by an idea for a film series centering on a diverse group of children banding together. The ghosts of Coalhouse and Sarah watch their son grow up (“Epilogue: Ragtime/Wheels of a Dream: Reprise”).