Photo: NBC

Here’s a fun exercise: Take a minute and count up all your friends. Not just the close ones, or the ones you’ve seen recently — I mean every single person on this Earth that you consider a pal.

Got a number in your mind? Good. Now cut it in half.

Okay, yes, “fun” may have been a bit of a reach there. But this new, smaller number may actually be more accurate. As it turns out, we can be pretty terrible at knowing who our friends are: In what may be among the saddest pieces of social-psychology research published in quite some time, a study in the journal PLoS One recently made the case that as many as half the people we consider our friends don’t feel the same way.

The study authors gave a survey to 84 college students in the same class, asking each one to rate every other person in the study on a scale of zero (“I do not know this person”) to five (“One of my best friends”), with three as the minimum score needed to qualify for friendship. The participants also wrote down their guesses for how each person would rate them.

Overall, the researchers documented 1,353 cases of friendship, meaning instances where one person rated another as a three or higher. And in 94 percent of them, the person doing the ranking guessed that the other person would feel the same way.

Which makes sense — you probably wouldn’t call someone a friend, after all, unless you thought that definition was mutual. That’s why we have terms to capture more one-sided relationships, like friend crush or hey, I don’t really know her but I think she’s neat. Both of which, come to think of it, might have been better descriptors of a lot of the relationships in the study. In reality, only 53 percent of the friendships — a small, sad, oh honey number of them — were actually reciprocal.

Some caveats: The study was small, and all the subjects were undergraduates; friendships change over the course of a lifetime, and it’s certainly possible that, over time, many tenuous lopsided friendships can dwindle to a more solid few. But the study authors also looked at a handful of previous surveys on friendship, ranging in size from 82 people to 3,160, and found similar results: Among those, the highest proportion of reciprocal friendships was 53 percent, and the lowest was a bummer, at 34 percent.

“These findings suggest a profound inability of people to perceive friendship reciprocity, perhaps because the possibility of non-reciprocal friendship challenges one’s self-image,” the study authors wrote. Fair enough. No one likes to think of themselves as the unwanted hanger-on, chasing a relationship that doesn’t really exist and maybe never will; this blind spot, then, may be a form of emotional self-defense. Luckily, though, it’s almost the weekend, so you’ll have plenty of time to give things a good hard look and question everything you thought you knew.