To hear the media tell it, America is in the grip of an unprecedented crime wave, an orgy of wanton murder in which heavily armed thugs randomly gun down innocent unarmed people, some of them teens, just for sport.

Except that these homicidal goons are wearing the blues and badges of American police departments.

It’s the narrative that’s given rise to the protest movement Black Lives Matter and to a growing public mistrust of the police in general. From Michael Brown in Ferguson, Mo., to the recent shooting of a middle-aged woman and a teen in Chicago, the body count seemingly keeps rising, exacerbating racial tensions and keeping the nation on edge. And each incident is breathlessly reported by a media determined to show that America remains deeply, irredeemably racist.

Problem is, it’s simply not true.

Last week, the Washington Post published a study of the police shootings that took place in 2015. Likely they intended the story to be shocking — as on Dec. 24, 965 people were killed by police! Instead, the report quells the notion that trigger-happy cops are out hunting for civilian victims, especially African-Americans. Among its key findings:

White cops shooting unarmed black men accounted for less than 4 percent of fatal police shootings.

In three-quarters of the incidents, cops were either under attack themselves or defending civilians. In other words, doing their jobs.

The majority of those killed were brandishing weapons, suicidal or mentally troubled or bolted when ordered to surrender.

Nearly a third of police shootings resulted from car chases that began with a minor traffic stop.

The moral of this story is: Don’t point a gun at the cops and don’t run when they tell you stop, and you’re likely to survive. Since the population of the US is about 318 million people, a thousand deaths at the hands of police works out to 1 in 318,000. You have a better chance of being killed in a violent storm (1 in 68,000) or slipping in the tub (1 in 11,500) than being shot by a cop, no matter what color you are.

But even these figures are deceptive. On those 965 killed, only 90 were unarmed, and the majority of those were white. (And that doesn’t take into account other extenuating circumstances besides a weapon that would have caused a police officer to fire.)

Still, the “killer cop” narrative refuses to die, and the Washington Post decided to throw fuel on the racial fire with context-free statements like these: “Although black men make up only 6 percent of the US population, they account for 40 percent of the unarmed men shot to death by police this year.”

This ignores the fact that black violent-crime rates are far higher than those of whites. According to the Department of Justice, blacks committed 52.5 percent of the murders in America from 1980 to 2008, when they represented 12.6 percent of the population.

This certainly does not excuse cases of police misconduct. Bad cops should be investigated and tried. The death of Walter Scott in South Carolina last spring — shot in the back while fleeing a white police officer after a routine traffic stop — resulted in the indictment of the cop, who is now awaiting trial. And the killing of Quintonio LeGrier and Bettie Jones in Chicago on Dec. 26, after the troubled LeGrier allegedly became “combative” with officers, cries out for further investigation.

But these incidents don’t prove that the “real problem” is cops. This isn’t an “epidemic.” And it isn’t racist to suggest that some perspective is warranted here.

Yet, encouraged by liberal politicians, the rhetoric of protesters has become more heated, poisoning relations between local police and the folks they serve. Most tragically, it’s resulted in the murders of police officers, such as NYPD Officers Wenjian Liu and Rafael Ramos, killed in a Brooklyn ambush just over a year ago.

Against the numbers cited by the Washington Post, what about this one: The worst neighborhoods in Chicago — say, West Garfield Park, where gangs run rampant — have a higher murder rate (116.7 per 100,000) than world murder capitals like Honduras (90.4).

But no, best not to mention. That only distracts from the real problem — the cops trying to stop it.