A teenager has been awarded more than $97,000 after a doctor ordered unnecessary surgery that left her permanently scarred.

The girl, now aged 14, sued the ACT government and a sports medicine physician for compensation but both defendants admitted negligence before the matter went to trial.

In a judgment published on Friday, Supreme Court Master David Harper found the girl was entitled to receive $97,596 for the way her fractured arm was treated after it healed in a deformed position. The girl was six-years-old when she fell off a chair at home in mid-December 2003 and fractured her left arm.

Her parents took her to Canberra Hospital where she received an X-ray and her arm was placed in a plaster slab before she was taken to see John Kellett, a sports medicine practitioner.

When Dr Kellett reviewed the girl in late January, a further X-ray revealed her forearm had set in such a way that it appeared deformed and was on a 30-degree angle.

The deformity was described as a ''banana arm''. Dr Kellett referred the girl and her parents to an orthopaedic surgeon and she had an operation to correct the deformity at John James Memorial Hospital in February 2004.

The operation inserted screws and plates into the girl's arm to stabilise the fracture but left her in considerable pain for some time.

Master Harper said the girl had to see her surgeon repeatedly in the months after the operation and in September was readmitted to hospital for another operation to remove the plates and screws.

For about a year afterwards the girl had muscle wasting in her arm and noticeable scars.

She sued the government and Dr Kellett and it was agreed she should have undergone a procedure known as a ''closed reduction'', which had previously been performed when she fractured her right arm earlier in 2003.

Master Harper found the girl had been ''subjected to what should have been unnecessary surgery and hospitalisation, with consequent pain and interference with her normal life''.

But he found she could only receive damages from the first operation to correct the deformity in her arm in February 2004.

''The plaintiff is thus not entitled to damages for the initial fracture, but only for the consequences of the negligent diagnosis and treatment,'' he wrote.

Master Harper found the girl now had no pain or restriction in her left arm but had been left with two scars - 12 to 13 centimetres long - on opposite sides of her forearm.

He said the scars were obvious, though not disfiguring, and noted that the girl might decide to have plastic surgery to lessen the scars when she was older.

Master Harper said the girl was fortunate to be part of ''an admirable and enviable family of five''.

But he briefly criticised the girl's lawyers for claiming compensation for 2311 hours of care from her parents, reducing the compensation to 100 hours of care at $21 an hour.

He praised the government and Dr Kellett for admitting liability and choosing to be represented jointly at the hearing, which reduced the cost of the hearing and the stress for the girl and her parents.