Rajinder Singh Rathore, a textile worker, and his daughters Karim, six, and twins Satnam and Marinder, four, died two hours after waving goodbye to their mother as they drove off to buy groceries.
Rakhbeer Kaur Rathore expected the family back in an hour but her husband drove to a filling station, bought pounds 7 of petrol and went to a secluded car park at the National Water Sports Centre in Holme Pierrepont, near Nottingham.
Detective Chief Inspector Harry Parfrement told the inquest that Mr Rathore poured petrol over the children in the rear passenger seats. He then doused himself, got back into the car and lit a match.
Witnesses heard a loud bang as the car exploded in a fireball. The victims had to be identified by their dental records.
Det Chief Insp Parfrement said Mr Rathore took off his turban and shoes and placed them on the floor in the front of the car just before striking the match.
He told Dr Nigel Chapman, the coroner, that he thought it was customary in Asian circles.
Mrs Rathore, of Radford, Nottingham, said the girls were laughing as they drove off with their father.
She said her husband had no financial or domestic worries and had not been depressed.
The dead man's brother, Suckhian Rathore, said: 'He was looking forward to the future all the time and was in the process of buying a house. He had asked me about mortgages and endowment policies.'
Mr Rathore's workmate and friend for five years, Richard Golder, said: 'I just can't understand why he did it.'
The coroner recorded verdicts that Mr Rathore committed suicide and unlawfully killed his children on 27 January this year.