One of the biggest questions in Financial Independence is how much do you need to retire? This is a question that could be answered a million different ways as everyone's situation is different. Spending habits, financial situation, and risk tolerance are all factors that play into how much you need to feel comfortable retiring early for your situation.
When talking about Financial Independence, most people are talking about reaching a point where you have enough passive cash flow from your investments (real estate, index funds, etc.) to cover your living costs. Typically, this is somewhere between $40,000 and $100,000 a year for a "normal" retiree. Above this range is considered "fat" and below is considered "lean". Below we go through the math behind reaching either of these goals.
Just as a quick side note, a lot of these number ranges are fuzzy. I am going off of some of the more widely accepted income ranges as to what constitutes Lean vs Fat Fire.
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The most commonly accepted definition of Lean FIRE is retiring and living off of $40,000 or less per year. Most commonly, people striving for Learn FIRE are frugal and live in low cost of living locales around the United States. To get to lean FIRE in 20 years or less, you need to be saving ~$15,000 a year which will put you right around $30,000 to $40,000 in today's dollars.
One sub-category of Lean Fire is what some call "barista FIRE" as well. This is where you can retire early, but to increase the longevity of your investments get a part time job that pays the bills. Barista FIRE is particularly common if you are staying lean as it gives you a good chunk of freedom in retirement, while not compromising your long term financial health.
If you are interested in Learn FIRE yourself, there are some great resources out there. The biggest community online for connecting with Learn FIRE people is the /r/leanfiresubreddit. It is filled with people asking questions about how to stay lean and retire as fast as possible.
Fat FIRE is the opposite of lean FIRE. The goal here is to accumulate a lot of wealth so that you can retire and live a "luxurious" lifestyle. As we mentioned before, this is often considered above $100,000 a year in spending. For some locations, this may be just enough to scrape by (looking at you San Francisco) while in other locations it will afford you a huge house with all the motorized toys you could want.
To get to Fat FIRE, you are going to have to save around $45,000 to $50,000 a year to reach the "minimum" threshold of $100,000 a year, or $4 Million in investments. This can be augemented by other investments that may give you cash per month like side businesses or owning rentals.
Fat FIRE proponents tend to rely a bit more heavily on investing in areas like Real Estate or Businesses in order to achieve their goals. On the /r/fatFIRE subreddit there is a lot of discussion around investing in assets that throw off cash versus the more "frugality" focused discussions on the lean FIRE subreddit.