WASHINGTON — Tipper Gore was more enraged about Bill Clinton’s affair with Monica Lewinsky than even Hillary Clinton, according to a new book.

“Tipper Gore was furious at Bill Clinton, angrier than Hillary Clinton was,” author Kate Andersen Brower told The Post. Her new book, “First in Line: Presidents, Vice Presidents and the Pursuit of Power,” comes out Tuesday.

With Lewinsky being the same age as the Gores’ eldest daughter, Karenna, Tipper “felt personally offended by the scandal,” said ex-Gore aide Jamal Simmons. The White House intern was 22 when the affair with Bill Clinton began.

“In Gore’s case there’s no way he would have gotten to such a dark place if Tipper hasn’t been so mad,” another aide told the author.

That “dark place” was Al Gore’s decision not to campaign with Bill Clinton during Gore’s 2000 run for the presidency, which – like Hillary Clinton – he lost because of the Electoral College math.

Hillary Clinton, on the other hand, used her husband’s White House record to vault into a US Senate seat in 2000, representing New York, becoming the first first lady to ever hold elected office.

Today, Al Gore still bristles when asked about his relationship with Hillary Clinton – who many characterized as Bill Clinton’s co-president, diminishing Gore’s role as veep.

“I expected him to say Hillary Clinton and I had a great working relationship,” Andersen Brower told The Post. Instead, “he thought the interview might have to be cut short,” she wrote in the book.

In the run-up to the 2016 election, Hillary Clinton’s top aide, Huma Abedin, had warned campaign chairman John Podesta and aide Cheryl Mills that Gore had said in 2015 that he wouldn’t be giving Hillary Clinton his endorsement.

Mills then offered that Gore might change his mind. “No. [It’s] bad,” Abedin replied in an email, which was part of the hacked conversations put online by Wikileaks.

Eventually, the endorsement did come, but in the form of a July 2016 tweet. He also never showed up to that summer’s Democratic National Convention.

Al Gore did, however, call Hillary Clinton after her 2016 election loss. ”She doesn’t need any advice from me,” he said to the author. “It was commiserating and reaching out to say, in her husband’s famous phrase, ‘I feel your pain.’”

Ron Klain, who served as both Al Gore and Joe Biden’s chief of staff, described the call to Andersen Brower as “nice” and “courteous,” but added, “I don’t think there’s been deep bonding.”

“They are both in that strange club of having won the popular vote and lost the Electoral College,” Andersen Brower pointed out.

They also were both negatively affected politically by Bill Clinton’s extracurricular sex life. President Trump turned the Democratic ex-president’s misdeeds into political fodder after he was exposed for saying that as a celebrity he could grab women “by the p—y.” Trump suggested that Hillary Clinton was complicit.

“They both suffered because of him,” Andersen Brower said, pointing to Hillary Clinton and Al Gore’s relationship with Bill Clinton.

Bill Clinton was in the news again Monday, revealing on the “Today” show that he never apologized personally to Lewinsky. “I apologized to everyone in the world.”

The book reveals that after denying the affair with Lewinsky to Al Gore in the entryway of the Oval Office, Bill Clinton eventually came clean to his vice president in the backseat of a limousine on Aug. 10, 1998, a week before the American public knew.

Bill Clinton told Al Gore that he was disappointed in himself. “Well, this is the first time you have apologized to me personally,” Al Gore answered.

After the confession, however, Bill Clinton was in a good mood, while Al Gore turned sour.

He was “upset, offended, and conflicted about what it all would mean for his own presidential ambitions,” Andersen Brower wrote.

Al and Tipper Gore, the author suggested, never recovered from his 2000 election loss.

The Gores separated in 2010.