Unless you’re one of the last remaining male-chauvinist tennis fans, it’s almost impossible to watch PBS’s inspiring documentary “American Masters: Billie Jean King” (airing Tuesday night) without a big smile on your face the whole time.

The sports legend, who turns 70 in November, had many triumphs on the court (six Wimbledon singles titles among them), but for a while it seemed history might remember King more for her courageous advocacy for women’s rights — especially her much-hyped “Battle of the Sexes” match against the vainglorious Bobby Riggs, an event that captured the nation’s attention when it took place 40 years ago.

But what “Billie Jean King” (written, directed and produced by James Erskine) shows us is that her feminism and her athleticism were never mutually exclusive; each worked as a near-perfect catalyst for social change. King is fond of noting that she played with her whole body, which included her mind.

She had, and still very much has, a way of resolutely articulating her vision of equality for all. As a film subject she has a true gift for gab and personal inquiry; as “Billie Jean King” was wrapping up, I was struck by the rare feeling of wanting the film to be longer, so we could keep listening to her talk about life, tennis, love and just about anything else. This makes it easy to overlook some of the fawning in “Billie Jean King,” courtesy of (frankly unnecessary) interviews with the likes of Hillary Rodham Clinton, Valerie Jarrett and Elton John.

The film begins with King’s idyllic upbringing in Long Beach, Calif., where, as an athletic girl, she despaired of ever playing sports until a classmate invited her to play tennis at a members-only club. Wearing a pair of requisite white shorts sewn by her mother for the occasion, young Billie Jean found the game strange and yet irresistible. Even as a teenager she says she was turned off by the sport’s lack of racial and class diversity.

Bobby Riggs posing for Billie Jean King. Riggs proudly proclaimed himself a male chauvinist pig as he hyped the 'Battle of the Sexes," played Sept. 20, 1973 at the Houston Astrodome. (AP/PRESS ASSOCIATION IMAGES/AP/Press Association Images)

“Billie Jean King” rightly concentrates on sports culture more than sports stats; if it had been produced by ESPN or HBO Sports, it would undoubtedly and helpfully have included more about how King actually learned to play tennis and perfect her game.

Instead, we go much too quickly from her first serves in suburban tennis camps to the pro circuit of the 1960s, which was then a sorry state of affairs for women, who earned next to nothing (and sometimes nothing), while their male peers took home sizable cash prizes. Even those who clearly remember King’s heyday will be struck, in hindsight, by the sexism she and her peers lived and played through.

King and others boldly parted ways with the sport’s status quo, signing on as the “Original Nine” players on the Virginia Slims women’s tennis circuit. This all happened at an exact right moment in history, dovetailing with women’s lib. “Use us,” King implored feminist leaders. “Use our bodies” to drive home the point that women work as hard as men.

This, of course, leads us to one of the more distracting and ridiculous watershed events in the struggle for gender equality: King’s showdown with Riggs, which was as much an act of theater as it was a game. “Billie Jean King” does a fabulous job of re-creating the excitement, tension and symbolic weight of the “Battle of the Sexes” and also unpacks some of its residual effects on American life. (Even now, there are some who suggest that Riggs deliberately threw the match.)

King left that court triumphant, but it turned out her most crucial test was still ahead, when her female assistant sued her and revealed that they had been lovers. It was 1981, and King, who was still married to her college sweetheart, chose to come out of the closet as a lesbian, at great financial cost. “I should have kept the letters,” she says, recalling the way her sponsors fired her. “They called me the worst names possible.”

The latter third of “Billie Jean King” is about soldiering on, focusing her efforts on promoting tennis and sportsmanship as well as civil rights. Eventually, the rest of the world catches up to King — a tennis arena was named for her; she was awarded a Medal of Freedom — but what’s most striking is how comfortable she is, then and now, in her own skin.

American Masters:
Billie Jean King

(90 minutes) originally scheduled to air at 8 p.m., will now air immediately after President Obama’s live address Tuesday on WETA.