windows3-2  Exercise 1: Three Relationships Among the Performance-Tab Figures
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Verification: Level 1 (read-only or short-lived allocation; run on the author's machine, no administrator rights).

Prediction (work this out before running the script):

  In use + Available equals usable RAM exactly, because In use is defined as the difference.
  Installed minus usable should be a couple of GB on a PC with integrated graphics and 32 GB
  installed (this is the memory reserved by hardware; I have not read Resource Monitor's own
  Hardware Reserved figure, so that part of the comparison is yours to make). Cached should be
  at least Modified + Standby, because Cached also includes Cache Bytes.

ex1.ps1 (run it with:  powershell -ExecutionPolicy Bypass -File ex1.ps1):

  # ex1.ps1: check three relationships among the Performance-tab figures.
  $total     = (Get-CimInstance Win32_ComputerSystem).TotalPhysicalMemory
  $installed = (Get-CimInstance Win32_PhysicalMemory | Measure-Object Capacity -Sum).Sum
  $names = 'Available Bytes', 'Cache Bytes', 'Modified Page List Bytes',
           'Standby Cache Normal Priority Bytes', 'Standby Cache Reserve Bytes', 'Standby Cache Core Bytes'
  $v = @{}
  foreach ($s in (Get-Counter ($names | ForEach-Object { "\Memory\$_" })).CounterSamples) { $v[($s.Path -split '\\')[-1]] = $s.CookedValue }
  $inUse = $total - $v['available bytes']
  $standby = $v['standby cache normal priority bytes'] + $v['standby cache reserve bytes'] + $v['standby cache core bytes']
  $cached = $v['cache bytes'] + $v['modified page list bytes'] + $standby
  'In use + Available = usable RAM?  {0:N3} + {1:N3} = {2:N3} GB' -f ($inUse / 1GB), ($v['available bytes'] / 1GB), (($inUse + $v['available bytes']) / 1GB)
  'Hardware reserved (installed - usable): {0:N2} GB' -f (($installed - $total) / 1GB)
  'Cached {0:N2} GB >= Modified + Standby {1:N2} GB?  {2}' -f ($cached / 1GB), (($v['modified page list bytes'] + $standby) / 1GB), ($cached -ge ($v['modified page list bytes'] + $standby))
  'Cache Bytes alone (the file-system cache working set): {0:N2} GB' -f ($v['cache bytes'] / 1GB)

Output (real, from the author's machine on 2026-10-24; your numbers will differ):

  In use + Available = usable RAM?  14.468 + 15.318 = 29.786 GB
  Hardware reserved (installed - usable): 2.21 GB
  Cached 12.93 GB >= Modified + Standby 12.31 GB?  True
  Cache Bytes alone (the file-system cache working set): 0.62 GB

WHY THIS WORKS AS AN ANSWER
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  The first line shows 14.468 + 15.318 = 29.786 GB, the usable RAM, so In use really is just
  "everything that is not available". Hardware reserved is 2.21 GB (32 - 29.79). Cached is 12.93 GB,
  at least the 12.31 GB of Modified + Standby, and the difference is the 0.62 GB of Cache Bytes, the
  file-system cache's own working set.
  The comparison with your real windows is the part only you can do. Plausible differences and
  their likely causes (not verified here): readings taken a second or more apart, because every
  figure moves; Task Manager showing a rounded or differently computed Cached or In use figure
  in Windows 11 compared with the Vista-era table Microsoft documents; and Resource Monitor's
  Hardware Reserved being reported in MB and possibly differing from installed - usable. Write
  down the numbers you saw rather than assuming they match.
  Common mistakes: adding Cached to Available (they overlap); using the 32 GB printed on the
  sticks instead of the usable figure for In use; and reading the counters in separate calls
  so that they drift between reads.