The result puts her in the top 1 per cent of the British population in terms of intelligence. Cowie, who has been offered scholarships to four prestigious fee-paying schools, said: "When I got the results, I was really surprised."
"It's quite daunting to be compared to great minds, but it feels good also to be thought of as that clever," the Daily Mail quoted her as saying.
"'I really enjoy puzzles and working things out and I think I'll go on to study sciences, especially biology, when I'm older." Cowie took the adult admission tests for Mensa, the society for people with a high IQ.
As well as surpassing brilliant scientists and Microsoft founder Gates, her score gives her a higher IQ than Sigmund Freud, who is thought to have had an IQ of 156, Napoleon Bonaparte, with 145, and Hillary Clinton, with 140.
Cowie's parents, who live in Claverley, near Wolverhampton, and run a health and safety consultancy, said they had always known their daughter was bright, but had not quite realised she was at genius level. Her mother Alison, 44, said she was proud of her daughter.
"When she was at nursery she had the reading ability of a child twice her age and she won science awards at school," Mrs Cowie said.
"We always knew she was clever - she was always in the top sets and her teachers always praised her - but we never quite thought she'd be in Mensa.
"She's just a normal child to us. She likes acting, dancing and singing and she's not the kind to always have her head stuck in a book," Mrs Cowie added.