The geometric and traditional centres of Sheffield. A field (left) and Sheffield Town Hall, the Crucible and Winter Garden (right). ‘Where the exact centre of a city lies is often hotly disputed,’ says Esri UK’s Ben Flanagan. ‘Some cities appear to have no acknowledged central point while others have multiple options’

Sheffield’s true centre lies towards the edge of the Peaks

The geometric and traditional centres of London. A spot over the road from De-Lady Salon in Lambeth (left) and Trafalgar Square with the King Charles I statue (right)

London’s real centre lies some way to the south-east of where it is commonly assumed to be. ‘Many central spots shift over the centuries and others stay put,’ says Flanagan. ‘Historically, central locations were used to measure the distances from city to city while residents would meet at different, popular focal points. But the analysis clearly shows the exact geometric centres – or where each city would balance on a pin – creating a whole new debate’

The geometric and traditional centres of Birmingham. An outdoor sports field at the Heartland’s Academy (left) and Victoria Square with the Town Hall (right)

Birmingham’s geometric heart is right beside Duddeston rail station

The geometric and traditional centres of Liverpool. Olive Grove (left) and the Town Hall (right)

Liverpool’s real centre is miles away from the Mersey

The geometric and traditional centres of Bristol. A residential address in Ravenswood Road and Broadmead shops (right)

Bristol’s real centre is up a steep hill from what is traditionally thought of as the town centre

The geometric and traditional centres of Newcastle. A garden in Quentin Avenue (left) and Grey’s Monument (right)

Newcastle’s real centre is a short hop from the airport

The geometric and traditional centres of Glasgow. A city map outside JD Sports (left) and George Square (right)

Glasgow’s real centre is close to Argyle Street

The geometric and traditional centres of Leeds. Gipton Wood (left) and Park Square with the Town Hall (right)

Leeds’s real centre is closer to the city golf club than the railway station

The geometric and traditional centres of Nottingham. Radford Boulevard (left) and the Old Market Square (right)

Nottingham’s real centre lies close to St Peter’s Park

The geometric and traditional centres of Manchester. Trautmann Close in a new development (left) and Albert Square (right)

Manchester’s real centre is in the Moss Side district