Its all about what your expenses are. If you can live on <$40K/year (which many people do) then you can live on $1M stashe ($1M x 4% = $40K). If you can live on <$20K/year then you only need ~$500K.
This! I have a stache of about $250K and could live on 4% ($10K/year) for all of my basic expenses. I also have a government pension of $1400/month that I live on easily without touching the $250K stash except for travel or emergency stuff. If one vanishes, I could live on the other (but together they are nice!). That is with a paid for house (co-owned with my sister and my share is worth approx. $250K), no debt, no kids, low expenses in the approx. $500 - $700/month range for basics (again, split with sister).
In addition, I plan to draw down on some (all?) of the principal over my life span since I have no one to leave anything too as well as sell my house and downsize dramatically freeing up some extra cash. This means I could have less in savings to live off of if I plan to use up the principal .
ETA: Changed my numbers above as I meant I had $500K in total assets (including house but not counting pension) not $500K in cash plus the house.
also ETA that I retired at 42 - over 10 years ago - and have never had any issues with COL or inflationary issues other then medical insurance cost increases. However, I only had a very inexpensive catastrophic plan (was cancelled in Jan due to the ACA) so never cost much and I also can get free or low cost medical thru the VA hospitals if needed.