Here's a historical look at the Linux market share on Steam, gathered using Valve's publicly provided data. Be sure to look over all the information, don't just take the first chart. If you have feedback, email us any time.

Note: Data from before September 2018 has been removed, due to a flaw Valve reported in the survey. Windows 7 machines were being over-counted since around August 2017, so there's no point keeping false data. See here for info. Then, Valve also reported another flaw in October, where smaller distributions were not being counted and the data for September was updated.

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For an estimation of the total number of Linux users on Steam, Valve reported they had 125 million "active" Steam users back in 2015. Considering Valve's rate of growth let's put that at 150 million active users now.

Using the latest months recorded share (Jan-2019 - 0.82%): 1,230,000 estimated Linux user total on Steam.
Once we get an up to date figure from Valve, we can update this.