Stephen Hawking, who sought to explain some of the most complicated questions of life while working under the shadow of a likely premature death, has died at 76.

He died peacefully at his home in the British university city of Cambridge in the early hours of Wednesday.

"We are deeply saddened that our beloved father passed away today," his children Lucy, Robert and Tim said in a statement.

Hawking's formidable mind probed the very limits of human understanding both in the vastness of space and in the bizarre sub-molecular world of quantum theory, which he said could predict what happens at the beginning and end of time.

His work ranged from the origins of the universe, through the tantalising prospect of time travel to the mysteries of space's all-consuming black holes.

"He was a great scientist and an extraordinary man whose work and legacy will live on for many years," his family said. "His courage and persistence with his brilliance and humour inspired people across the world."

The power of his intellect contrasted cruelly with the weakness of his body, ravaged by the wasting motor neurone disease he developed at the age of 21.

Hawking was confined for most of his life to a wheelchair. As his condition worsened, he had to resort to speaking through a voice synthesiser and communicating by moving his eyebrows.

The disease spurred him to work harder but also contributed to the collapse of his two marriages, he wrote in a 2013 memoir My Brief History.

In the book he related how he was first diagnosed: "I felt it was very unfair - why should this happen to me," he wrote.

"At the time, I thought my life was over and that I would never realise the potential I felt I had. But now, 50 years later, I can be quietly satisfied with my life."

Hawking shot to international fame after the 1988 publication of A Brief History of Time, one of the most complex books ever to achieve mass appeal, which stayed on the Sunday Times best-sellers list for no fewer than 237 weeks.

He said he wrote the book to convey his own excitement over recent discoveries about the universe.

"My original aim was to write a book that would sell on airport bookstalls," he told reporters at the time. "In order to make sure it was understandable I tried the book out on my nurses. I think they understood most of it."

He was particularly proud that the book contains only one mathematical equation - relativity's famous E=MC squared.

"We have lost a colossal mind and a wonderful spirit," said Tim Berners-Lee, the inventor of the World Wide Web. "Rest in peace, Stephen Hawking."

Hawking's popular recognition became such that he appeared as himself on the television shows Star Trek: Next Generation and The Big Bang Theory, and his cartoon caricature appeared on The Simpsons.

A 2014 film, The Theory of Everything, with Eddie Redmayne playing Hawking, charted the onset of his illness and his early life as the brilliant student grappling with black holes and the concept of time.

Hawking was Lucasian Professor of Mathematics at Cambridge University from 1979 to 2009 - a post held by Sir Isaac Newton over 300 years earlier - wrote countless scientific papers and books, received 12 honorary degrees and was made a Companion of Honour by Queen Elizabeth in June 1989.

To celebrate turning 60, he satisfied a life-long ambition and travelled in a specially created hot air balloon.

He narrated a major segment of the opening ceremony of the London Paralympic Games in August 2012, the year he turned 70.

"I have had a full and satisfying life," he said in his memoir. "I believe that disabled people should concentrate on things that their handicap doesn't prevent them from doing and not regret those they can't do."

He added: "It has been a glorious time to be alive and doing research in theoretical physics. I'm happy if I have added something to our understanding of the universe."