Last week, I looked at the status of the legal marijuana market in Colorado following the release of a blockbuster report from the state’s Department of Revenue reviewing the first few months of legalization. A key finding of the report was that a substantial amount of the recreational market is composed of Coloradans moving from the black market to the retail market.

On one hand, this is a story about the success of decriminalizing an activity a lot of people do and pulling a lucrative business out of the shadows. But it also had me wondering about how many pot dealers there are in the United States. Counting them turns out to be a difficult problem, and a Google search turned up a bunch of useless Yahoo Answers about legalization.

Instead, I approached the question through a technique called Fermi estimation, a back-of-the-envelope strategy that is generally good about making sure you’re in the right order of magnitude if not exactly correct. You’re probably somewhat familiar with it if you’ve ever heard the classic interview question, “How many piano tuners are there in the city of Chicago?”

First, break the problem into parts. You estimate the demand (the number of piano tunings needed in Chicago in a year), and then given the demand, you estimate the supply (the number of piano tuners) needed to meet that demand. How many people are in Chicago? Given that, how many households? How many households with a piano? How often does a piano need to be tuned? How many pianos can a piano tuner tune in a week? So, how many piano tuners do you need to satisfy demand?

The answer won’t be perfect, but the objective is to get it in the ballpark. Are we talking dozens of piano tuners? Hundreds? Thousands? That’s what Fermi estimation is good at.

Back to marijuana. How many full-time pot dealers are there in the United States?

I looked at the 2011 National Survey on Drug Use and Health from the federal Substance Abuse and Mental Health Services Administration to get a headcount of people who smoke marijuana. According to the survey, 29.7 million Americans 12 or older had smoked within the past year. Of those, 18.1 million smoked pot within the past month. For our purposes, let’s assume the people who smoked within the past month are regular users, and the rest are occasional users. This means that in 2011, about 11.6 million smoked at least once a month, and 6.5 million people had used marijuana less than once a month. The report also estimated that 7.1 million people 12 or older used marijuana more than 20 times per month.

So this is what our demand for marijuana looks like:

Use, but less than once per month: 11.6 million occasional users

Use between one and 20 times per month: 11.1 million regular users

Use more than 20 times per month: 7.1 million heavy users

It’s important to draw these lines when it comes to usage, because it makes a difference when it comes to estimating how frequently people buy pot. Because we’re estimating the number of full-time pot dealers, we only want to look at the regular and heavy smokers; I’m going to assume that people who use pot less than once per month probably get it from friends.

For the next step, I assume that heavy marijuana users buy from a dealer twice a month, regular users buy once a month and infrequent users don’t buy from a professional pot dealer. This estimate is partially informed by consumption data I read in a RAND Corp. study, but mostly because it seems a reasonable frequency.

This means that 11.1 million people are buying weed once a month, and 7.1 million people are buying weed twice a month. This comes out to 29.2 million professional marijuana transactions per month in the United States. Let’s guess that a full-time pot dealer works every day, eight hours a day and can make one transaction per hour; that comes out to about 240 sales per month per pot dealer.

There’s a lot of liability for error in this estimate — that pace seems a bit speedy for a pot dealer, and it also assumes that pot dealers don’t run out of marijuana — but as long as we’re in the right order of magnitude of “a couple of hundred drug sales per month,” we’re in the ballpark.

With 29.2 million marijuana transactions per month and 240 transactions per dealer, division says that we’d need 121,600 pot dealers to satisfy demand. This seems surprisingly reasonable. That’s a little less than the number of family physicians in 2011.

So, how does this stack up against other metrics of the drug salesman profession? Again, we sought to estimate the minimum number of people required to satisfy the market, but unsurprisingly the actual number may very well be higher. Based on FBI statistics, there were about 94,900 arrests for marijuana sale or manufacturing in 2011. And while this number accounts for the entire marijuana production apparatus in the U.S. — at all steps in the chain, from producers to major traffickers to low-level part-timers — it’s unreasonable to expect that the nearly 121,600 estimate is exactly right. But hey, at least our source isn’t Yahoo Answers.

CORRECTION (July 17, 12:01 p.m.): A previous version of this post incorrectly classified the NSDUH’s 18.1 million figure as annual users. In fact, the NSDUH found that 18.1 million people had smoked marijuana within the last month; 29.7 million people had used marijuana within the lsat year. The error has been corrected — as have dependent numbers.