Philip, now 19 years old, returns home from college and picks a fight with George Eacker, a man who gave a speech insulting Hamilton. They agree to a duel but Philip goes to Hamilton for help, not knowing what to do.
On the day of the duel, Phillip plans to aim his gun at the sky in order to not kill anyone, but still prove his bravery. Eacker, however, fires at Philip on the count of seven instead of ten, hitting him.
Philip is taken to hospital, but his wound becomes infected before he arrives, meaning his odds of survival are slim. Both Hamilton and Eliza come to the hospital and Eliza sings to Philip in the style of their old piano and French lessons as he dies.
In mourning for their son, Hamilton begs for Eliza’s forgiveness, knowing that they need each other to get through such a tragedy. She forgives him and they make amends. Angelica and the ensemble are amazed at the reconciliation.
It is the election of 1800. Burr is running against Jefferson for president and Madison worries that Jefferson is too opinionated on subjects such as France and that this might end up pushing voters away. Madison advises Jefferson to try and get Hamilton’s support. Hamilton disapproves of Burr's tactics and lack of support. He publicly endorses Jefferson for this reason, driving the final wedge into his and Burr’s old friendship.
Burr and Hamilton exchange letters, Burr furious that Hamilton would endorse Jefferson over him, despite the fact that they have hated each other for years. Hamilton refuses to apologize and Burr challenges him to a duel.
Hamilton leaves for the duel, accidentally waking up Eliza as he writes a farewell letter. Eliza tries to convince him to come back to sleep but Hamilton insists he has to leave.
Certain that Hamilton will not only fire on him but win, Burr prepares for his defeat. He admits to being a terrible shot, and Hamilton seems intent on winning as evidenced by the fact that he “methodically fiddled with the trigger,” and is wearing his glasses in order to have better aim. Hamilton, however, is yet undecided about what he should do. He questions what a legacy is, finally sure that he will be remembered and that “someone will sing” for him. He sees a vision of the afterlife and knows that he cannot fire on Burr, instead aiming his pistol at the sky just as he told Philip to do. Burr sees this and realizes his mistake but it is too late.
Hamilton dies in the hospital with Angelica and Eliza at his side. He finally realizes that his actions will ensure his legacy forever, and that the world was “wide enough” for him.
The musical comes to an end as we hear the characters' last thoughts on Hamilton. Eliza tells us about the next 50 years of her life and how she was the one to tell Hamilton’s story. She interviews soldiers, such as Lafayette and Mulligan, and tells their stories. She raises funds in order to commemorate Washington with the Washington Monument, and speaks out against slavery, just as Laurens would have wanted. Finally, she moves on to building her own legacy, the first private orphanage in New York City. She says that she sees Alexander in the eyes of all these children, raising hundreds of them until her own death. Finally, she addresses Alexander, saying that she cannot wait to see him again in the afterlife.
The conflict is not over for Hamilton, and soon after his affair is revealed to his wife, his young son is shot in a duel for defending his father's honor. Hamilton, once a plucky and fearless young man, must come to terms with the tragedies and unpredictable nature of life, and the loss of his son is a horrible blow to his well-being and sense of self. After so much hardship, this is yet another difficulty that Hamilton must endure in his already difficult life.
A positive outcome to come out of the death of his son is Hamilton's reconciliation with Eliza. As they both mourn the premature loss of their boy, Hamilton suggests that they ought to mourn together, as their grief is shared. Though she has been gravely disappointed by Hamilton's actions, Eliza ends up forgiving him, and they come together once again. While the loss of Philip is devastating, it serves to bring the husband and wife back together to mutually support one another.
Hardship is not far behind, however, and Aaron Burr's promise from the opening number that he would be the one to shoot Hamilton comes true in this final section. Burr and Hamilton's rivalry has been a fairly benign one up until recently. But after various betrayals, Hamilton chooses to endorse Jefferson for president, gravely offending his old friend, Burr, who promptly challenges him to a duel. The tensions that have built up because of the two men's vastly different approaches to politics come to bear, and they arrive at a tragic impasse.
The "duel," a social convention common in the 18th century, comes to represent this impasse between rivals. In a duel, one man must die, and it becomes an unpredictable psychological game of chance. Dueling is, in many ways, like a more decisive, violent version of the rap battle, in that it pits two men against each other to explicate their differences and determine a winner. In the rap battle, Hamilton is a worthy foe because of his facility with language and rhetoric. In a duel, however, he is without his usual defenses, and so resorts to surrender, shooting his gun at the sky.
Hamilton's surrender in the duel, although it leads to his death, solidifies his honorable reputation in history and connects him with his son, Philip, whom he advised to do the same in his own duel. In shooting towards the sky and not towards his old friend, Hamilton signals to the world and to the writers of history that he is willing to die for what he believes in and he does not want to kill Aaron Burr. In choosing to surrender himself in the duel, Hamilton secures his legacy and connects to his role as a father to the fallen Philip.