The study is the first UK-wide to assess the scale of the problem. It found one in ten children experienced at least three such traumatic events in their lifetime.
Boys are at the greatest risk, along with those from low-income households and those with younger mothers.
Researchers examined the incidence of seven types of adverse experience among more than 3,000 children.
The most common negative experiences involved parents having mental health problems or relationship break-ups, affecting around one-third of children.
Almost one-quarter of youngsters experienced frequent physical punishment, and one in five felt unloved or emotionally neglected.
Some 14 per cent had been exposed to parental drug or alcohol misuse, while one in ten had been exposed to domestic violence.
One in 250 children had a parent being sent to prison. Instances of sexual abuse were too few to be reported.
Boys were more likely to have had three or more traumatic experiences, as were those whose mothers had fewer educational qualifications and lived in deprived areas.
The research is published in the journal BMJ Paediatrics Open.
It is based on the Scottish Government-funded Growing Up In Scotland study, tracking children from birth through their teenage years and beyond.
Researchers interviewed parents, and later children, every one to two years.
Dr Louise Marryat, research fellow at the university’s centre for clinical brain sciences, said: “We know adverse experiences in childhood are associated with physical and mental health problems in later life.
“This is the first study to assess the scale of the problem in a current population of young people in the UK.
“We hope the findings will help to explain the context of ACEs [adverse childhood experiences] and lead to increased support for the groups most at risk.”