WASHINGTON -- Donald Trump said his inauguration will have "an unbelievable, perhaps record-setting turnout."

Organizers of a protest the next day call it the biggest demonstration in history to welcome a new president.

Exactly how many people show up for both events likely never will be known.

Million Man March

For decades, the National Park Service provided official crowd estimates for gatherings on the National Mall.

That changed after the Million Man March in 1995, a gathering of black men meant to show renewed commitment to family and solidarity. The park service estimated 400,000 people attended the march, making it one of the largest demonstrations in history in Washington.

But organizers believed they reached their goal of 1 million participants. Nation of Islam leader Louis Farrakhan, one of the march organizers, threatened to sue the park service over the count. Researchers at Boston University did an independent analysis and said the crowd was bigger, pegging it at more than 800,000.

No lawsuit was filed, but the dispute was enough to get the park service out of the head-counting business.

How they're counted

Before it stopped, the park service came up with its crowd figures by studying aerial photographs.

Using a grid system, the park service would divide the Mall into sections of equal square footage. Then it counted the number of people in each section of the grid by looking at how tightly packed the crowd was and assigning a number of people per square foot.

Not much has changed since about the way crowds are estimated, said Steve Doig, a journalism professor at Arizona State University who specializes in measuring crowd sizes.

The figure that corresponds to a "loosely packed crowd," Doig said, is 10 square feet per person, "which sounds like a lot, but it's really not." That means people could reach out and touch those closest to them on all sides.

Christopher Geldart, the District of Columbia's homeland security director, consistently has said he expects between 800,000 and 900,000 people to attend Trump's inauguration. He said he would use the grid method to provide his own crowd estimate on the Monday after the swearing-in.

Women's march

The largest-ever demonstration in Washington, according to park-service figures, was an anti-Vietnam War protest in 1969 that drew 600,000. The Mall easily can accommodate crowds in the hundreds of thousands; between 300,000 and 400,000 regularly attend the July Fourth fireworks.

Organizers of Saturday's Women's March on Washington have received a permit from D.C. police for a gathering of 200,000 people.

Past inaugurations

The park service did not dispute a widely reported estimate 1.8 million people came to Washington for President Barack Obama's first inauguration in 2009, believed to be the largest inaugural crowd in history. The biggest crowd the park service counted at an inauguration was 1.2 million for Lyndon Johnson's 1965 swearing-in.

Anytime a crowd reaches into the hundreds of thousands, it's a noteworthy gathering, Doig said, but boosters always try to politicize the turnout for their chosen cause.

"One of the things that aggravates me ... is the need for it to be huge," he said. "It sort of drives the numbers into areas where it just clearly is fiction, and it undercuts the reality of what really is an amazing crowd."

Trump clearly cares about posting a big number.

In a video ad posted on social media Wednesday, he said: "Hopefully we're going to get a million people. We're going to really make a big statement."