That's up from 35 per cent in 2014.
The Pew Research Center says that 66 per cent of respondents have witnessed other people being harassed.
While some people's experiences could be "shrugged off" as a nuisance, some 18 per cent said they were subjected to "severe" forms of harassment.
This included physical threats, stalking and harassment over a sustained period.
The vitriol of the 2016 presidential election has brought the issue to the forefront for many people.
Twitter and other online companies have promised to crack down on abuse.