there's been a lot of studies. Here's one group in the US

The true extent is unknown because it's not as commonly reported as you might imagine. There are a lot of people who accept abuse as normal relationships.

But one thing that needs to be looked at, and should be sobering is how quickly people are to latch onto the idea that men are awful. For example, in the US, women are actually more likely to be abuse children than men (and elsewhere, I found one study that said 70% of abuse cases were perpetrated solely by mothers or both parents. I don't entirely trust that study, or I'd link it.)

Domestic violence and who perpetrates an who the victims are... is much more complicated than people realize. While it's clear that men are more likely to initiate serious domestic violence- and that women are more likely to only resort to domestic violence in self defense or retaliation- it gets pretty messy pretty quickly. For example, in the abstract for this study:

• women’s violence usually occurs in the context of violence against them by their male partners;
• in general, women and men perpetrate equivalent levels of physical and psychological aggression, but evidence suggests that men perpetrate sexual abuse, coercive control, and stalking more frequently than women and that women also are much more frequently injured during domestic violence incidents;
• women and men are equally likely to initiate physical violence in relationships involving less serious “situational couple violence,” and in relationships in which serious and very violent “intimate terrorism” occurs, men are much more likely to be perpetrators and women victims;
• women’s physical violence is more likely than men’s violence to be motivated by self-defense and fear, whereas men’s physical violence is more likely than women’s to be driven by control motives;
• studies of couples in mutually violent relationships find more negative effects for women than for men; and
• because of the many differences in behaviors and motivations between women’s and men’s violence, interventions based on male models of partner violence are likely not effective for many women.

While I make no claim to the accuracy of that study... there's also a lot of bad "studies" that seem to demonize one or the other- or defend one or the other. I would tend to trust the NCADV stats I linked first, mind, which paints a pretty clear picture when it comes to violence against partners and whose doing it.

One of the things that's incredibly frustrating is when you realize that most men who are abused by their partner will almost certainly not report it to police. because of shame, because they may not even realize it's violence. Because cops might arrest you if they say you attacked first (and that fat lip from where you hit back is rather compelling.) A lot of women also don't report, Most. probably. Because we live in a fucked up world.

and this all just the physical abuse. Wait until you find out how horribly under reported psychological abuse is.