As Mikkel Hartmann, the cook aboard the Danish merchant ship Rozen, anxiously awaits his upcoming reunion with his wife and child, he finds himself caught in a dire situation when the ship's engineer, Jan Sørensen, asks him to deliver a letter to his family. Back in Denmark, a representative named Lars Vestergaard is caught in a high-stakes game of sealing a vital deal with Japanese businessmen. Desperate for assistance, he consults Peter Ludvigsen, the CEO, who eventually manages to secure the agreement. Unfortunately, their moment of triumph is abruptly overshadowed by alarming news: the Rozen has been overtaken by pirates in the treacherous waters of the Indian Ocean.
Amidst the chaos of the hijacking, Hartmann is coerced at gunpoint to prepare a meal for his captors, while automatic gunfire echoes around them, keeping all hostages in a state of constant dread. Determined to ensure the safe return of his crew, Ludvigsen engages the services of Connor Julian, an adept Australian hostage negotiator famed for his tactical skills in confronting pirate threats. Although Julian suggests employing a neutral third party for better negotiation, Ludvigsen is resolute in addressing the issue directly himself.
The first contact with the pirates occurs when Omar, a Somali who claims to be a translator taken hostage, urges Hartmann to reach out to Ludvigsen. However, Ludvigsen dismisses the communication and cuts the call short. Unyielding, Omar takes the initiative to convey the pirates' demands, which leads to Ludvigsen's initial counter-offer—a number so absurdly low that it signals a daunting negotiation ahead.
As the days unfold slowly, the pirates occasionally bestow upon their hostages certain privileges, such as bathroom access. Hartmann and Sørensen attempt a friendly rapport with one of their captors, only to experience humiliation when their gestures go unreciprocated. With provisions beginning to run low, Hartmann becomes increasingly frustrated, prompting Omar to cut off contact for resupply and demand that Hartmann reach out to Ludvigsen again. Yet, Ludvigsen refuses to communicate through Hartmann, leaving the crew hanging in uncertainty.
The tense negotiations progress at a snail's pace, with Omar expressing disbelief over Ludvigsen's unyielding low offers, cautioning that this ongoing impasse can only lead to further suffering and potential death if a realistic agreement isn't struck promptly. The pressure of these demands weighs heavily on Ludvigsen, culminating in an emotional outburst directed towards his concerned girlfriend. As the situation spirals out of control, the fate of the Rozen crew rests in the balance.
When the pirates finally allow the hostages some time on deck, Hartmann seizes a rare moment of hope, reeling in a large catch that elicits cheers from both captives and captors. The atmosphere is enlivened by the rhythmic chants of sea shanties, evoking the spirit of the ocean itself. In a touching moment of connection, Hartmann shares that it's his daughter’s birthday, triggering a spontaneous group rendition of "Happy Birthday to You." Later on, Omar grants Hartmann a fleeting reunion with his wife Maria, which is abruptly cut short by an aggressive pirate, who demands that she pressure Ludvigsen for compliance with their demands. The response from Ludvigsen only invites more ridicule from the pirates.
As the impasse continues, Ludvigsen feels isolated and increasingly frustrated, especially as he becomes detached from Julian’s advice. When Omar warns that violence might soon ensue among the pirates, a gunshot rings out, deeply unsettling Ludvigsen as he contemplates his own responsibility in Hartmann's safety. The pressure escalates as the board of directors, unhappy with the stalled negotiations, threatens to replace Ludvigsen unless he can finalize an agreement before the end of the month.
Amid this turmoil, Ludvigsen receives a fax from the pirates, compelling him to seek proof of Hartmann’s continued survival. Sørensen's subsequent disclosure reveals the harrowing treatment Hartmann has endured—an unrelenting mix of psychological and physical abuse, leaving him emotionally raw. As negotiations renew, Ludvigsen proposes an amount of $2.8 million, but Omar rejects it outright. Vestergaard suggests enhancing the offer by pretending to include his own funds, eventually persuading Omar to accept.
Onboard the ship, Omar gathers all the hostages on deck, allowing them to reunite for the first time since their ordeal began. A plane flies overhead, releasing a package that sends waves of excitement through the pirates as they eagerly retrieve it. As tension declines, Hartmann finally regains possession of his wedding ring, which he had concealed when the pirates attacked. However, the jubilance is short-lived when one of the pirates snatches the ring away, only to be struck down by Omar in an act of discipline.
In the aftermath, Sørensen breaks down in tears over the fallen captain's body, while Omar reprimands the errant pirate for his recklessness. Back in Denmark, Ludvigsen faces the heartbreaking task of informing the captain's widow of the tragic outcome, leaving him reeling from the enormity of the situation. As Hartmann finally embraces his family once more, he appears emotionally detached, still wrestling with the profound psychological scars left by his harrowing experiences at sea.
