How many people in the United States are poor? It's a surprisingly tricky question.

The "official" poverty rate was 15 percent in 2012. That number gives the impression that poverty is a bright line, that roughly one sixth of the country is poor and the rest are not poor. But that's a bit misleading. As a new report from the Census Bureau shows, a much, much larger subset of people slip in and out of poverty all the time.

For instance: Between 2009 and 2011, nearly one third of the country — 31.6 percent — fell below that official poverty line for at least two months. By contrast, only 3.5 percent of the U.S. population remained poor for that entire period. Both of those figures rose after the recession:

"A small fraction of people are in poverty for more than 1 year," writes Ashley Edwards, author of the census report, "while a larger percentage of people experience poverty for shorter time periods." In the years after the recession, the median length of time spent in poverty was 6.6 months.

The poverty rate we usually see quoted — the 15 percent figure — is the "annual poverty rate." That's calculated by "comparing the sum of monthly family income over the year to the sum of monthly poverty thresholds for the year." (The official poverty line is defined as $23,492 per year for a family of four.) So a family that had very little income for four months and then earned more money the remaining eight months might not count as poor for the year, even though they went through a significant period of hardship.

Here are the different ways that the census measures poverty over the past few years:

By any count, the recession made poverty significantly worse. Persistent, chronic poverty rose from 3 percent to 3.5 percent. Many more Americans experienced brief spells of poverty. The median length of time spent below the poverty line also increased, from 5.7 months before the recession to 6.6 months after.

There was also a fair bit of churn. In the first two months of 2009, there were 37.9 million people in poverty. About one third of them, 12.6 million, managed to escape poverty by 2011 — although many were still hovering close to the poverty line. And that improvement was counterbalanced by the fact that 13.5 million people who weren't poor in 2009 became poor by 2011.

By the way, the Census study above is looking at the "official" poverty rate, a metric that comes in for plenty of criticism. But the Census has developed other "experimental" measures, too. There's also this alternative measure of poverty developed by researchers at Columbia University that tries to be more comprehensive and arrives at somewhat different results. That Columbia study also found that poverty rose during the recession — but that it would have risen much more sharply had it not been for safety net programs such as food stamps, unemployment insurance and Medicaid.

Related: Everything you need to know about the war on poverty