Google has so far kept mum on the numbers, though Google executive chairman Eric Schmidt has said there are "millions" of users on the service.
A number of users have attempted to unofficially gauge the success of the site by using a variety of metrics to estimate just how many users it has so far.
It should be noted that Google Plus launched as a "limited field test" and is being gradually rolled out to users -- thus far, it is available only by invitation. Still, according to Google Plus user Paul Allen, founder and CRO of the popular Facebook application FamilyLink, Google Plus reached 11.5 million users as of Tuesday night and grew by 22 percent in 24 hours. This estimate uses one-third of the sample size of his previous samples and should be treated with less confidence than his previous estimates, Allen noted.
Allen previously announced when Google Plus had, by his calculations, reached 4.5 million and 10 million users. The growth rate in the last 24 hours "compares favorably" to his previously published growth rate of 30 percent in a 32-34 hour period, Allen told The Huffington Post by email Tuesday night.
Allen (unrelated to the Microsoft founder), is a serial entrepreneur who previously founded the website Ancestry.com and is now the chief financial officer of FamilyLink. He has taken an interest in estimating the Google Plus user count and calls himself an unofficial Google Plus statistician on his Google Plus profile.
He has been estimating the Google Plus growth rate by comparing the number of names on Google Plus to the number of names in the 2000 U.S. Census.
First, he takes a sample of 100 obscure names from the 2000 U.S. Census surname database and then counts how many times those names appear on Google Plus among United States users. He uses a second set of 100 obscure names to double check his work. (For this latest sample, he only performed 38 queries, which is why he is less confident in his results.)
Second, using a ratio of name appearances on the U.S. Census to name appearances on Google Plus, he estimates the total number of users on Google Plus in the United States. Third, using a ratio of Google Plus users in the U.S. to international users that he determined by looking across a sample of names, he finds the total number of Google Plus users.
This methodology has some potential sources of error. Google Plus users might be biased toward certain types of names, given that the community is filled with early tech-adopters who, as a consequence of the invite process, are closely tied with the other users, noted technology entrepreneur Arun Shroff. Second, the 2000 U.S. Census data is old. Nevertheless, Allen's estimate methodology is a promising attempt at counting Google Plus users.
Other users have been estimating the size of Google Plus based on the search result count of Google query: inurl:plus.google.com/*about site:plus.google.com. However, this estimate is unreliable for several reasons. First, the query returns not only Google profiles, but also posts by Google users, noted Allen. As detailed by Search Engine Land editor-in-chief Danny Sullivan, Google search result counts have been known to give inaccurate results.
Another Google Plus user, Zubin Wadia, used the ratio of Google Plus traffic to Gmail traffic to estimate Google Plus users based on Gmail users. Gmail had 193.3 million users when it publicly released its user count in November 2010. Extrapolating to the present day based on previous Gmail growth rates, Zubin estimated that its current user count is 245 million users. From there, using the ratio of Google Plus traffic to Gmail traffic as measured by Alexa, a web traffic information site, he estimated that Google Plus had 8.91 million users by Tuesday night. The third-party site Alexa was used because Google doesn't publicly release traffic estimates. Zubin said he "picked Gmail because it parallels the usage patterns of Google Plus vs. say G-Search," he told The Huffington Post.
This estimate methodology has some potential sources of error. First, Zubin's Gmail user extrapolation and Alexa's traffic counts could be inaccurate. Second, the difference in Google Plus to Gmail usage patterns may bias the data.
Only Google knows the real numbers. What's clear from anyone monitoring Google Plus is that the service is experiencing rapid growth. That being said, total users and growth metrics might not be the best way to evaluate the success of the service. What really matters for the service's long-term success is what these users do after they sign up.
UPDATE 7/14 4:53 PM: Larry Page just announced that over 10 million users have joined Google Plus.