Fairbanks, Alaska, residents participate in the Farthest North Women’s March on Washington on Jan. 21, 2017. (Robin Wood/Fairbanks Daily News-Miner via AP)

This is the fifth post in our series on what social science can tell us about the Women’s March on Washington. Here are the firstsecond, third and fourth. — TMC editors

The Women’s March on Washington was likely the largest single-day demonstration in recorded U.S. history. The only potential competitors were the Vietnam War Moratorium days in 1969 and 1970, which boasted millions of participants worldwide (and up to 1 million in the United States). The first Earth Day in 1970, which some claim had between 10 million and 20 million participants, did involve some demonstrations, but much of the activity involved local educational workshops and science fairs held at schools. And in February 2003, an estimated 10 million people demonstrated worldwide in opposition to the U.S. invasion of Iraq, with around 1 million of those marching in the United States.

Here’s how we counted

We arrived at these figures by relying on publicly reported estimates of march locations and the number of participants involved in each. We started a spreadsheet and called for crowdsourced information about the location and number of participants in marches. Before long, we had received thousands of reports, allowing us to derive low and high estimates for each event. We carefully validated each estimate by consulting local news sources, law enforcement statements, event pages on social media, and, in some cases, photos of the marchers. When reports were imprecise, we aimed for conservative counts; for example, if observers reported “hundreds” of participants, we reported a value of 200 (“thousands” was 2,000, “tens of thousands” was 20,000, etc).

From this, we counted at least 653 reported marches in the United States. These involved huge gatherings of well over 100,000 marchers in Washington; Los Angeles; Oakland, Calif.; San Francisco; New York; Chicago; Denver; Seattle and Boston.

But there were some places with surprisingly high turnout. For instance, in Wyoming, eight marches brought out between 3,800 and 5,000 people statewide. And in Alaska, 25 marches mobilized nearly 9,000 people statewide.

In total, the women’s march involved between 3,267,134 and 5,246,670 people in the United States (our best guess is 4,157,894). That translates into 1 percent to 1.6 percent of the U.S. population of 318,900,000 people (our best guess is 1.3 percent).

To put this in perspective, the combined armed forces of the U.S. military — including the Air Force, Army, Navy, Marine Corps reserves, National Guard, and Coast Guard — comprise just over 2 million people.

How strongly were people motivated to protest?

After a story came out with the headline that 1 in 100 Americans had marched, some critics noted that the other 99 did not.

True, during an election for president or Congress, winning one of 100 votes would be a poor performance. But this misses the meaning of protest numbers. Marching requires a much higher level of commitment than voting. It takes more time, is not anonymous, often involves financial costs and could put the marcher in harm’s way or at risk of arrest or retaliation — particularly in areas where the marchers are expressing a minority sentiment.

In some instances, marchers had to overcome serious limits on mobility to join, suggesting highly intense motivation. For example, five people marched in the cancer ward at a Los Angeles-area hospital. Fifty women marched in a retirement community in Encinitas, Calif. And 415 women’s mobility was so limited that they participated in the women’s march online.

Braving harsh weather was another test of intense motivation. In Alaska, 2,000 people marched in Fairbanks with a high temperature of 19 below zero; in Unalakleet, 38 or 40 people marched despite a windchill of 40 below. One woman in a Western mountain state was snowed in and couldn’t get to the nearby town where she intended to march. Instead of giving up, she held a march of one in her own town.

There were marches everywhere in the U.S.

Our count revealed that the women’s march took place in areas that were urban and rural, red and blue. About 68 percent of the marches had 1,000 or fewer participants. Overall, there were 297 marches in states Trump carried in the election, with between 721,000 and 1,005,000 total marchers. In red states such as Montana and Alaska, many people marched — if you use “many” to mean more than 1 percent of the state’s population using low estimates. Among the thousands of submissions received as people sought to fill in the spreadsheet, we could feel a palpable sense of pride among Montanans for the 10,000-strong attendance at the Helena march.

If you look at the marches’ size and locations as a map, it contrasts sharply with the news media’s usual electoral map that makes the country look starkly divided.

Sister marches took place around the world, as well

The Women’s March on Washington had sister marches in international locales ranging from Antarctica to Zimbabwe. We found at least 261 marches abroad, with attendance totaling between 266,532 and 357,071 people (our best guess is 307,275 people).

Observers should take these marches seriously, too. Transnational solidarity often gives a movement more leverage than a purely domestic movement might otherwise have. Moreover, it can be powerful and emboldening when activism is witnessed by others at home and abroad.

We don’t know yet whether this transnational solidarity will help the U.S. protest movement; most of the research to date has been on movements elsewhere that get support from U.S. activists.

What did the marches mean?

We don’t want to overestimate the power of a single march, however large. A march won’t have much effect unless it’s translated into continuing organized and disciplined mobilization, pressure on the government, collaborative problem-solving and electoral action. But if a march inspires, convenes and energizes, it can catalyze a great deal of change. Very large movements are more likely to translate their goals into real political, social and political change, particularly as they expand their networks into leverage.

These marches reveal momentum or insight from earlier movements, such as Black Lives Matter, Standing Rock, climate action, immigrant rights, the tea party, trans rights, and Occupy Wall Street. As others have argued here recently, U.S. conditions are ripe for more women’s — and other — protests in the coming months and years.

We will keep counting

Documenting the women’s march in real time, we learned how important it was for people to be seen, witnessed and counted. Because accurate information on popular participation helps gauge their progress and latent power, we are launching a Crowd Counting Consortium (CCC) that will aim to continually keep track of how many people are protesting. We already have live spreadsheets underway cataloging the periods Jan. 22 — Feb. 5, and Feb. 6 — Feb. 19, 2017.

The CCC is not a research project. It’s a public service. To see more about the CCC, check out the website.

Erica Chenoweth is a professor at the Josef Korbel School of International Studies at the University of Denver. Oxford University Press will publish her next book, “Civil Resistance: What Everyone Needs to Know,” early next year. Find her on Twitter @EricaChenoweth.

Jeremy Pressman is an associate professor of political science and director of Middle East Studies at the University of Connecticut. Find him on Twitter @djpressman.

Note: This post has been updated to include the Coast Guard amongst the branches of the U.S. military.