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 90 million "monthly active users" in January 2019 (source).

Using the latest months recorded share (Sep-2019 - 0.83%): 747,000 estimated "monthly active users" for Linux Steam.

To be clear, that is not the total, that is monthly active.