In 1963, Cambridge University astrophysics student Stephen Hawking (Eddie Redmayne) begins a relationship with literature student Jane Wilde (Felicity Jones). Although Stephen excels at mathematics and physics, his friends and professors are concerned over his lack of a thesis topic. After Stephen and his professor Dennis Sciama (David Thewlis) attend a lecture on black holes, Stephen speculates that black holes may have been part of the creation of the universe and decides to write his thesis on time.
While pursuing his research, Stephen’s muscles begin to fail, eventually causing him to fall and hit his head. He learns he has motor neurone disease; he will be unable to talk, swallow, breathe or move most of his body, and has approximately two years to live. Stephen asks what will happen to his brain. The doctor tells Stephen that the disease doesn’t affect the brain and that Stephen’s thoughts won’t change but eventually, no one will know what they are. As Stephen becomes reclusive, focusing on his work, Jane confesses her love to him. She tells Stephen’s father she intends to stay with Stephen even as his condition worsens. They marry and have a son.
Stephen presents his thesis to the examination board, arguing that a black hole created the universe in a Big Bang, that it will emit heat, and that it will end in a Big Crunch. While celebrating with Jane and his friends, Stephen realises he cannot walk and begins using a wheelchair.
After having a second child, a daughter, Stephen develops a theory about the visibility of black holes and becomes a world-renowned physicist. While focusing on the children, Stephen’s health and his increasing fame, Jane is unable to work on her own thesis and is frustrated; Stephen tells her he understands if she needs help. She joins the church choir, where she meets widower Jonathan (Charlie Cox). She and Jonathan become close friends, and she employs him as a piano teacher for her son. Jonathan befriends the entire family, helping Stephen with his illness, supporting Jane, and playing with the children.
When Jane gives birth to another son, Stephen’s mother asks Jane if the baby is Jonathan’s. Jane is appalled; seeing that Jonathan overheard the conversation, when they are alone they admit their feelings for one another. Jonathan stays away from the family, but Stephen visits him, saying that Jane needs him.