The risk that children would be prescribed too low a dose rose with age, but younger children were also at risk of being prescribed too high a dose.
A team led by Dr James McLay and colleagues from Royal Aberdeen Children's Hospital studied data on 4,423 prescriptions for children issued in 2006.
'The reasons for these prescribing patterns are unclear,' the researchers said. 'However it is possible that in the absence of reports relating to underdosing and treatment failure, primary care physicians have been sensitised by earlier reports of paracetamol overdosing and hepatotoxicity.'
The risk of harm from treatment not working and failing to reduce pain or fever as a result of underdosing is often overlooked, the researchers stated.
The researchers also said that their data could not show whether or not doses had been taken and so whether under or overdosing had occurred.