They were also more likely to be "fairly" or "very" upset by the content, the number for females was 38 per cent compared to 18 per cent for males.
Meanwhile, older teenagers were exposed to potentially harmful content more often than those aged around 13 to 14 years.
Younger children could be protected by parental software but it was a different story for older ones, Netsafe chief executive Martin Cocker said.
"We live in an imperfect world, where risks exist and young people will often be exposed to them on their devices away from the eyes of their parents," he said.
"Younger children can be monitored and protected by parental software, but older children will choose who they disclose incidents to, and who they will seek help from."
But following the discovery of upsetting content online, the study found 11 per cent of children decided not to speak with anyone.
The majority of respondents would speak to a parent, 69 per cent in fact, while 37 per cent would speak with a friend and 17 per cent a sibling.
It was a "big step" if young people stepped forward for help and people needed to be readily available for them, Cocker said.
"We know from previous research that young people fear they will be punished and their caregivers will blame them for the situation they find themselves in," he said.
"This is something young people believe stems from adults not taking the time to understand the online world they inhabit.
"If a child comes to you it is important to focus on fixing the issue and providing them with the right support to help minimise the harm they may experience."
A total of 2061 children aged between 9 and 17 years of age took part in the study, with the sample a representative of the population of New Zealand children.
Where to get help: • Netsafe: 0508 638 723 (available seven days a week) • Lifeline: 0800 543 354 (available 24/7) • Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7) • Youth services: (06) 3555 906 • Youthline: 0800 376 633 • Kidsline: 0800 543 754 (available 24/7) • Whatsup: 0800 942 8787 (1pm to 11pm) • Depression helpline: 0800 111 757 (available 24/7) • Rainbow Youth: (09) 376 4155 • CASPER Suicide Prevention If it is an emergency and you feel like you or someone else is at risk, call 111.