In 2002, their convictions were vacated when another man confessed to the crime and a DNA match proved he had committed it.

In their documentary “The Central Park Five,” directors Ken Burns, his daughter Sarah Burns, and her husband, David McMahon, recount the story of the crime, the effect it had on an entire city, and on the lives of the five boys. The film, which opens here on Friday , also shows how the confessions were coerced.

“I’m so tired,” Ken Burns said over a bowl of dumplings at a restaurant near Fenway Park last month. Burns long ago became a cultural brand name, thanks to such PBS documentary series as “The Civil War,” “Baseball,” and “The War,” about World War II.

Burns’s latest, “The Dust Bowl,” had recently been broadcast. The night before, he’d presented an award to newscaster Tom Brokaw at Old Sturbridge Village. In an hour, he’d be appearing at a fund-raiser for the Epilepsy Foundation. “I’m 59 years old and a grandfather now,” he laughed. “What’s going on here? This is the busiest and most insanely creative I’ve ever been.”

Q. Why this particular subject? Why now?

A. My daughter has been interested in this [case] for almost a decade. First as an undergraduate at Yale, writing a final thesis, then writing a book on it. As the first pages were coming out, it seemed really clear that there was a film there.

Q. Is it possible to divvy up credit?

A. Sarah was both a novice filmmaker and an utterly experienced one, having watched her mom and dad make films from the very beginning. Dave ran the day-to-day production. I did a lot of interviews. Dave did a lot of interviews. Sarah did a lot of interviews. We all made the decisions collectively, along with our superb editor, Michael Levine.

Q. There’s a jitteriness to the editing, especially to the first half-hour, 45 minutes. It’s so intense.

A. And consciously so, because that was the times. We were all kind of crack addicts, we were all kind of worried about what would happen to us on the way to or from work. Then it settles in the experience of the interrogations. It takes on another pace, with those videotaped confessions; then yet another, around the trial; and yet another, at their incarceration. Then you have this extraordinary denouement.

Q. Did working with family members feel different?

A. You might think, that movie has three directors: How bad is that? How many screaming matches? What Sharpies were thrown across the editing room? In fact, none of that happened. It was always clear what path [to follow]. Plus, it’s my daughter, my baby. I’d be sitting in the same room listening to her conduct an interview. I did my first interview on a sync-sound camera in January of 1972, and I still feel like a student. And here you are listening to your baby do it, and do it really well!

Q. The documentary tells a story that, in so many ways, is awful.

A. Awful.

Q. What I found most affecting was, from the point of view of a parent, inevitably thinking, what if my son had been one of these kids? Maybe the most powerful moment, for me, was when Raymond [Santana]’s father says —

A. “I sent him into the park that evening.” This has been very moving for me to work with my daughter. Also very moving to get to know these five —

Q. Who are such impressive men.

A. Incredibly impressive. With a noticeable lack of overwhelming bitterness. With a kind of weariness, but also wisdom. We’ve been out on the road with them appearing before audiences, and it suddenly felt as though we were merging families.

Q. Do you remember your response to the story at the time?

A. I do indeed.

Q. You were working on “The Civil War.”