The calculator
$40,000 a year at 4.0% is $1,000,000. From $200,000 plus $20,000 a year at 5.0% real, that is 17.4 years.
How it works
Lean FIRE at this page's $40,000 default is a $1,000,000 nest egg at 4%. From $200,000 invested plus $20,000 a year at 5% real, that is a little over 17 years of saving. Fat FIRE is the same identity at a larger spend — $150,000 a year is $3,750,000, not a different formula.
Same identity as every other FIRE number: spending divided by the withdrawal rate. The years figure inverts the ordinary-annuity future value. The Fat FIRE calculator is the other end of the same scale. Coast and Barista are the milestones on the way: Coast FIRE calculator, Barista FIRE calculator. The generic identity is the FIRE calculator.
Assumptions
Contributions at year end, one real return, no fees, no taxes. The default spending figure is a reference point, not a recommendation.